[Kpt-Ahab] Candles Slot MachineHow the Game Works
Candles Slot Machine** is an automated slot machine simulation that runs directly on the PulseWire chart.
Each new game starts with 100 credits:
1. Disable Autoplay to reset the game and change the settings.
2. Set the maximum number of spins under Autoplay bars.
3. Select the wager per spin under Bet per spin.
4. Enable Autoplay to start the game.
5. Exactly one spin is completed at each confirmed close of a real-time bar.
The wager is deducted from the available credits on every spin. Three symbols are then generated, and any applicable payout is calculated.
A game ends when:
* the selected maximum number of spins has been reached, or
* there are not enough credits remaining for the next wager.
The final result remains visible for three fully completed bars. The next game then starts automatically with another 100 credits. The cumulative session statistics remain active until Autoplay is disabled, which resets the entire session.
Symbols and Payouts
Each symbol has its own probability:
* **Cherry:** 30%
* **Lemon:** 25%
* **Bell:** 18%
* **Star:** 13%
* **Seven:** 9%
* **Diamond:** 5%
Two matching symbols pay x1. This only returns the original wager, resulting in a net outcome of zero for that spin.
Three matching symbols pay:
* **Cherry:** x6
* **Lemon:** x8
* **Bell:** x12
* **Star:** x20
* **Seven:** x40
* **Diamond:** x100
Three Diamonds form the jackpot.
The payout model has a theoretical RTP of 92.53%. This value represents the expected long-term payout relative to all credits wagered. It does not guarantee any particular outcome for an individual game or a short session.
Random Generation
The reel symbols are generated using a combined pseudo-random calculation. The script uses, among other inputs:
* runtime random values
* individual game and spin numbers
* confirmed OHLCV data from the current bar
* bar closing time and bar index
Market data is used exclusively as additional entropy for the random-generation process. It is not evaluated as a trading signal, and there is no intended relationship between price direction and game results.
The script is not designed to simulate historical spins retroactively. New spins are executed exclusively on confirmed real-time bars.
Game Speed
The speed of the game depends directly on the selected chart timeframe because one spin is completed per confirmed bar close.
Examples:
* On a 1-minute chart, approximately one spin is completed per minute.
* On a 15-minute chart, approximately one spin is completed every 15 minutes.
* On a 1-hour chart, approximately one spin is completed per hour.
Exchange closures, missing market updates, or unconfirmed bars delay the next spin accordingly.
Indicator
Strategy Forecast EngineThe Strategy Forecast Engine is a regime-based Monte Carlo forecasting tool that estimates the future return distribution of trend-following strategies across different market environments. The model identifies the current market regime, conditions forecasts on historical returns observed during comparable regimes, and generates thousands of potential future price paths using Monte Carlo simulation. The resulting return distribution is presented through percentile projections and a structured, color-coded table that provides a comprehensive assessment of the forecast.
First, the model identifies the current market regime using the selected trend-following strategy. Users can choose between a moving-average crossover strategy, a volatility-based trailing stop strategy, or a combined strategy that incorporates both approaches. Supported moving-average types include the Exponential Moving Average (EMA), Simple Moving Average (SMA), Wilder’s Moving Average (RMA), and Weighted Moving Average (WMA). Supported volatility types include the Average True Range (ATR), Standard Deviation (SD), and Mean Absolute Deviation (MAD). By default, the model applies an asymmetric design in which conflicting signals default to bullish unless neutral regimes are enabled in the menu. Market regimes are determined as follows:
Bullish Trend Regime = (Fast MA – Slow MA) > (ATR × Trend Margin)
Bearish Trend Regime = (Fast MA – Slow MA) < –(ATR × Trend Margin)
Bullish Volatility Regime = Price > (Highest Price – (Volatility × Stop Factor))
Bearish Volatility Regime = Price < (Lowest Price + (Volatility × Stop Factor))
Bullish Combined Regime = Bullish Trend Regime and Bullish Volatility Regime
Bearish Combined Regime = Bearish Trend Regime and Bearish Volatility Regime
Once the current regime has been identified, the model collects all historical logarithmic returns that occurred during the same regime beginning from the selected start date. Only returns from the matching regime are used to generate the forecast, allowing projections to be conditioned on historically comparable market environments rather than treating all historical observations as equally relevant. If duration-adjusted forecast is enabled in the menu, the model further restricts the sample pool to returns from regimes that were at least as mature as the current regime.
The Monte Carlo simulation engine then generates thousands of possible future price paths over the selected forecast horizon. Each simulation randomly samples historical returns from the sample pool associated with the current regime and compounds them forward to generate a potential future price path. This process is repeated for the specified number of simulations to produce a broad range of possible future outcomes. The random seed controls reproducibility, ensuring that identical settings produce identical forecasts. Once all individual simulations have been completed, the resulting return distribution is summarized using percentile projections:
95% = 5% of simulations ended above this level and 95% ended below it.
75% = 25% of simulations ended above this level and 75% ended below it.
Median = 50% of simulations ended above this level and 50% ended below it.
25% = 25% of simulations ended below this level and 75% ended above it.
5% = 5% of simulations ended below this level and 95% ended above it.
The upper quartile (75%) and lower quartile (25%) define the Interquartile Range (IQR), which contains the middle 50% of all simulated outcomes and represents the central range of the projected outcome distribution. The upper and lower tail percentiles can be set to 10% (90% / 10%), 5% (95% / 5%), or 1% (99% / 1%). The default setting is 5%, which captures the middle 90% of simulated outcomes. At 10%, the range captures 80% of simulated outcomes, while at 1%, the range captures 98% of simulated outcomes. To further evaluate the risk/reward characteristics of the forecast, the model includes a built-in table with the following metrics:
Regime = Current market regime based on the selected strategy configuration.
Duration = Percentile rank of current regime duration relative to past regimes.
Forecast = Percentile rank of current duration including the forecast horizon.
Win Rate = Percentage of profitable simulations relative to total simulations.
Profit Factor = Ratio of total simulated profits to total simulated losses.
Expectancy = Average expected percentage return across all simulations.
Reward/Risk = Ratio of upper quartile return to lower quartile return.
Asymmetry = Ratio of selected upper tail return to selected lower tail return.
Skewness = Ratio of upside potential to downside risk relative to the median.
Sample Size = Number of historical returns available for the current regime.
Frequency = Percentage of historical returns belonging to the current regime.
In summary, the Strategy Forecast Engine is a comprehensive forecasting tool designed to help investors evaluate the return distribution of trend-following strategies based on the current market regime. By combining regime detection with Monte Carlo simulation, the model conditions forecasts on historical returns observed during comparable market regimes to estimate the distribution of potential outcomes and their associated risk/reward characteristics. While the model provides valuable insight into historical return patterns, investors should remain mindful that historical market behavior may not necessarily persist under future market conditions. Indicator
Complex Single Trade StrategyThis 'Complex Single Trade Strategy' is a generic trading strategy that features three different types of stops, and four take profits.
It takes a Buy/Sell source input of:
The first signal will trigger a position to open immediately in that direction, but subsequent signals in the same direction will be ignored whilst the position remains open, as this strategy allows only one position at once.
A signal in the opposite direction to the current position can either be ignored, or it can close the position, or it can close it then immediately open another one in the opposite direction.
It also takes an optional 'Cancel' indicator just to close positions. Other signals will be ignored.
The three different types of stops, that can be applied individually, or together:
* Regular Stop
* Initial Trailing Stop
* Trailing Stop
The initial trailing stop works like a regular trailing stop until it reaches the cut off level, a percentage of the current asset price above or below the entry level, then it will no longer trail the price, remaining statically at this level.
From here the regular trailing stop can take over trailing the price. This is useful to move the stop to the entry level (or there abouts) fairly quickly. From there you might want to trail the price with a larger trailing stop for the rest of the trade.
0 cut off means it stops trailing the price at your entry level, positive above, negative below, for a long trade. For a short it would be the opposite.
Typically you would want:
Trailing Stop > Initial Trailing Stop >= Stop
The four take profits each specify an amount to reduce the position size by, and at what specified percentage gain in price this is triggered.
My 'Simple Buy/Sell Indicator' and 'Custom Buy/Sell Indicator' (coming soon - watch this space) can be used to combine other indicators together into BUY/SELL strategies, using multiple custom rules. These can then be used as inputs to this strategy.
Strategy
Predictive Monte Carlo Engine [LuxAlgo]The Predictive Monte Carlo Engine tool is a high-performance forecasting suite that uses probabilistic simulations to project future price paths based on historical volatility and market regimes.
🔶 USAGE
The indicator generates hundreds of potential price paths starting from the current bar (or an anchored point) to visualize the most likely price distribution over a user-defined projection length. It serves as a powerful volatility and support/resistance mapping tool, providing traders with an "expected value" range rather than a single fixed forecast.
Users can choose between three distinct mathematical methods to generate these paths, apply regime filters to isolate specific market conditions, and utilize a real-time dashboard that renders a visual "forecasted candle" for the next period.
🔹 Anchor Mode
By default, the simulation recalculates and updates on every new bar. By enabling Anchor Mode , users can lock the projection starting point. The engine will then only update every X bars (e.g., every 100 bars). This allows traders to observe how price actually reacted against historical Monte Carlo projections and Support/Resistance levels as the chart progresses.
🔶 DETAILS
The engine utilizes three primary simulation methodologies:
Geometric Brownian Motion (GBM): A stochastic process that assumes returns follow a log-normal distribution. This is the industry standard for modeling asset prices, ensuring prices remain positive and incorporating both drift and volatility.
Simple Random Walk (SRW): A basic additive model where price changes are sampled from a normal distribution based on historical mean and standard deviation.
Historical Shuffle (Bootstrapping): Instead of using random numbers, this method randomly samples actual historical price returns from the lookback period. This preserves the "fat tails" and unique characteristics of the specific asset being traded.
🔹 Regime Filtering
To improve accuracy, the engine can filter the historical data used for simulations. If "Trend" or "Momentum" regimes are selected, the indicator only calculates volatility and drift from past bars that match the current market environment (e.g., only using data from previous uptrends to forecast a current uptrend).
🔹 Fading S/R Zones
The tool identifies four key levels based on the simulation distribution: Max, R1 (90th percentile), S1 (10th percentile), and Min. These are rendered as horizontal zones that feature a unique horizontal gradient, fading as they extend into the future to represent the increasing uncertainty of the projection over time.
🔶 SETTINGS
🔹 Monte Carlo Settings
Simulation Method: Choose between GBM, SRW, or Historical Shuffle.
Regime Filter: Filter historical data by Trend (SMA) or Momentum (RSI).
Historical Lookback: The number of past bars used to calculate volatility.
Projection Length: How many bars into the future the paths extend.
Simulation Count: Number of individual paths to calculate (max 200).
Volatility Multiplier: Scales the historical volatility to simulate "stress-test" scenarios.
Anchor Mode: When enabled, locks the projection to update only at specific intervals.
🔹 Style
Path Percentiles: Adjust the thresholds for coloring the "Top" and "Bottom" path groups.
Colors: Customize the colors for bullish, bearish, and neutral paths, as well as the average projection line.
Show S/R Levels: Toggles the visibility of the horizontally fading Support and Resistance zones.
🔹 Dashboard
Show Dashboard: Toggles the statistical metrics table.
Next Candle Prediction: Enables the "Forecasted Candle" visual, which uses the 1-bar-ahead expected mean and distribution to render a text-based candlestick on the dashboard.
Indicator
Monte Carlo Expected Move Distribution [LuxAlgo]The Monte Carlo Expected Move Distribution indicator is a statistical forecasting tool that uses Geometric Brownian Motion (GBM) to simulate hundreds of potential price paths, generating a vertical probability distribution to visualize where the market is mathematically expected to trade within a specific future timeframe.
🔶 USAGE
The indicator provides a forward-looking "Expected Move" profile, a concept widely used in options trading to determine the implied range of an asset. It helps traders move away from single-line price predictions and toward a probabilistic understanding of market outcomes.
🔹 Setting Realistic Price Targets
By looking at the vertical distribution at the end of the projection, traders can identify the "Median Outcome" (50th percentile). This represents the most likely price level based on current trend (drift) and volatility.
Conservative Targets: Aim for levels within the highlighted "Expected Move" (1-SD) area.
Aggressive Targets: Levels sitting in the "tails" (gray areas) are statistically less likely to be reached within the chosen timeframe.
🔹 Identifying Overextensions
The dashed projection lines represent the upper (+1 SD) and lower (-1 SD) boundaries.
Upper Expected Move: If price reaches this level ahead of the projection time, it is considered "overbought" relative to current volatility.
Lower Expected Move: If price drops to this level rapidly, it is considered "oversold" from a statistical standpoint.
🔹 Understanding the Distribution Profile
The vertical histogram (bins) at the right of the chart represents the density of the simulations. The widest part of the histogram shows the price zone where the highest number of simulated paths ended, indicating the highest mathematical probability for that price area.
🔶 HOW TO USE
To use the indicator effectively, follow these steps to align the statistical model with your trading timeframe:
Define Your Horizon: Adjust the "Projection Length" to match your trade duration (e.g., 20 bars for a swing trade or 5 bars for a scalp). The distribution will shift further into the future accordingly.
Evaluate the Drift: Enable "Include Trend (Drift)" if you believe the current price momentum will persist. If you expect a sideways market or a "random walk," disable this setting to center the distribution on the current price.
Analyze Probability Zones: Look at the colored region of the histogram. If your target price lies within this zone, there is a ~68% statistical probability (based on current volatility) of price reaching that area within the specified time.
Risk Management: Use the Lower Expected Move (-1 SD) as a guide for stop-loss placement in long positions, as prices falling below this level represent an outlier move beyond normal volatility expectations.
🔶 DETAILS
The script utilizes Monte Carlo Simulation via Geometric Brownian Motion. This model accounts for two primary factors:
Log-Volatility: Derived from the standard deviation of historical log-returns, determining how "wide" the potential price swings are.
Drift (Optional): An approximation of the current trend based on a moving average, providing a directional bias to the simulations.
The "Expected Move" is defined as the 1-Standard Deviation range (the 16th to 84th percentiles). In a normal distribution, approximately 68% of all outcomes fall within this range. The indicator highlights this specific zone in color, while the outliers (the remaining 32%) are shown in a neutral gray.
🔶 SETTINGS
🔹 Monte Carlo Simulation
Simulations: The number of paths to generate (50-500). Higher values result in a smoother, more accurate distribution profile.
Projection Length: How many bars into the future the "Expected Move" is calculated for.
Volatility Lookback: The period used to measure historical price fluctuations.
Include Trend (Drift): When enabled, the distribution will lean toward the current trend direction. When disabled, it assumes a mean-neutral random walk.
🔹 Distribution Visuals
Price Bins: The vertical resolution of the histogram. More bins allow for a more detailed view of the probability peaks.
Distribution Color: Sets the color for the "Expected Move" (68% probability) zone.
Max Distribution Width: Controls how many bars wide the histogram is drawn on the chart.
Indicator
Monte Carlo Mean Reversion Heatmap [LuxAlgo]The Monte Carlo Mean Reversion Heatmap indicator is a statistical forecasting tool that uses Geometric Brownian Motion (GBM) to simulate 100+ potential future price paths and visualize the mathematical probability of price returning to a specific mean.
🔶 USAGE
The indicator provides a visual "probability cloud" projecting from the current price into the future. It helps traders identify statistical overextensions and the likelihood of a trend reversal toward a long-term average.
🔹 1. Assessing Mean Reversion Probability
The dashboard shows a Mean Reversion % . This tells you how many of the 100 simulated paths "touched" or "crossed" the EMA ribbon within the projection window (e.g., the next 30 bars).
High Probability (>70%): If the current price is far from the EMA but the probability of reversion is high, it suggests the market is "overextended." You might look for a counter-trend trade back toward the EMA.
Low Probability (<30%): This suggests that volatility is so high or the trend is so strong that price is statistically unlikely to return to the mean anytime soon. This often happens during "parabolic" runs.
🔹 2. Trading the "Probability Fan"
The dotted lines (5%, 50%, 95%) represent the statistical boundaries of where price is expected to stay.
Overbought/Oversold: If price moves outside the 5% or 95% lines, it is making a move that only happens in 1 out of 20 scenarios. This is a "statistical extreme." Traders often look for reversals or profit-taking when price enters these outer edges of the cone.
The Median Path (50%): This dashed line represents the "most likely" path based on current momentum (drift). It serves as a realistic target for trend-following trades.
🔹 Heatmap Density
The heatmap represents the density of the simulated paths. Darker areas indicate a higher concentration of paths, marking the price zones with the highest mathematical probability of being reached according to the model.
🔶 DETAILS
The engine behind this script is the Geometric Brownian Motion (GBM) model. GBM is a continuous-time stochastic process used in mathematical finance to model stock prices.
The model assumes that price changes follow a random walk with two components:
Drift: The deterministic trend of the mean (directional bias).
Volatility: The random "noise" or shocks based on historical log-returns.
By running 100 individual simulations simultaneously, the script generates a distribution of outcomes rather than a single linear prediction. This allows the user to see the "width" of uncertainty in the current market environment.
🔶 SETTINGS
🔹 Mean Calculation
Mean Length: The period of the EMA used as the target for mean reversion analysis.
Mean Color: The color of the target EMA line on the chart.
🔹 Monte Carlo Simulation
Simulations: The number of random paths to calculate (higher values increase accuracy but may impact performance).
Projection Length: How many bars into the future the simulation projects.
Volatility Lookback: The window used to calculate historical log-volatility for the simulation.
Include Drift: When enabled, the simulation accounts for the slope (trend) of the Mean EMA.
🔹 Visuals
Price Bins: Determines the vertical resolution of the heatmap.
Heatmap Color: The base color used for the probability density cloud.
Show Percentile Lines: Toggles the visibility of the 5%, 50%, and 95% projection lines.
🔹 Dashboard
Show Dashboard: Toggles the statistical information table.
Position/Size: Controls the location and scale of the dashboard on the chart.
Indicator
Indicator Configuration Forecasting [LuxAlgo]The Indicator Configuration Forecasting tool identifies historical market regimes that share a similar technical configuration to the current market and projects future price action based on those historical outcomes. By encoding multiple technical indicators into a state vector and employing a K-Nearest Neighbors (KNN) search, the script provides a probabilistic forecast including a median path and confidence intervals.
🔶 USAGE
The indicator works by "memorizing" the state of various user-selected technical indicators at every bar. When the current bar's configuration matches or closely resembles a previous historical state, the script records how the price moved in the subsequent N bars from that point in time.
🔹 Forecast Interpretation
Median Forecast (Dashed Gray): Represents the 50th percentile (median) of all matched historical outcomes. This is the central tendency of the forecast.
Upper Bound (Dashed Green): Represents the 75th percentile of historical outcomes, suggesting a bullish boundary for the projected move.
Lower Bound (Dashed Red): Represents the 25th percentile of historical outcomes, suggesting a bearish boundary for the projected move.
Match Labels: Small labels appearing on the historical price action indicate exactly where the most similar configurations were found in the past.
🔹 Configuration Strategy
Users can toggle various indicators to define what constitutes a "similar" market state. For example, if only "SMA Cross" and "Supertrend" are enabled, the script will look for historical periods where the trend relationship and SMA positioning were identical to the current bar, regardless of RSI or MACD values.
🔶 DETAILS
The script utilizes a state-encoding methodology to calculate distances between the current market environment and the past. Each enabled indicator is converted into a discrete value (e.g., 1 for bullish, -1 for bearish, 0 for neutral). These values form a vector for the current bar.
The algorithm then scans through the "Historical Lookback" period to find the "Top K" neighbors—the points in history where the vector distance to the current state is minimized. To ensure variety in the forecast, the script includes logic to prevent overlapping matches, ensuring that the selected historical points are distinct events.
Once the matches are identified, the script calculates the percentage returns for the specified "Forecast Horizon (N)" and projects those returns onto the current price to generate the visual forecast.
🔶 SETTINGS
🔹 Parameters
Top K Neighbors: The number of similar historical configurations to include in the forecast calculation.
Forecast Horizon (N): How many bars into the future the forecast should extend.
Historical Lookback: The maximum number of historical bars the script will search through to find matches.
🔹 Indicator Configuration
RSI/SMA/Supertrend/MACD/ADX/etc.: Toggle switches to include or exclude specific technical conditions from the similarity search.
RSI: Looks for similar overbought (>70) or oversold (<30) states.
SMA Cross: Looks for similar Fast/Slow SMA relationships.
Supertrend: Matches the current direction of the Supertrend.
MACD: Matches the relationship between the MACD Line and Signal Line.
🔹 Visibility & Style
Show Individual Match Paths: When enabled, draws the actual historical price paths from the match points directly on the current chart for visual comparison.
Median/Upper/Lower Colors: Customizes the colors of the forecast lines and the shaded confidence intervals.
Dashboard: Toggles the information panel showing the number of matches found and forecast confidence.
Indicator
Range Breakout Statistics [Honestcowboy]⯁ Overview
The Range Breakout Statistics uses a very simple system to detect ranges/consolidating markets. The principle is simple, it looks for areas where the slope of a moving average is flat compared to past values. If the moving average is flat for X amount of bars that's a range and it will draw a box.
The statistics part of the script is a bit more complicated. The aim of this script is to expand analysis of trading signals in a different way than a regular backtest. It also highlights the polyline tool, one of my favorite drawing tools on the pulsewire platform.
⯁ Statistics Methods
The script has 2 different modes of analyzing a trading signals strength/robustness. It will do that for 2 signals native to the script.
Upper breakout: first price breakout at top of box, before max bars (100 bars by default)
Lower breakout: first price breakout at bottom of box, before max bars
The analysis methods themselves are straightforward and it should be possible for pulsewire community to expand this type of analysis to other trading signals. This script is a demo for this analysis, yet some might still find the native signals helpful in their trading, that's why the script includes alerts for the 2 native signals. I've also added a setting to disable any data gathering, which makes script run faster if you want to automate it.
For both of the analysis methods it uses the same data, just with different calculations and drawing methods. The data set is all past price action reactions to the signals saved in a matrix. Below a chart for explaining this visually.
⯁ Method 1: Averages Projection
The idea behind this is that just showing all price action that happened after signal does not give actionable insights. It's more a spaghetti jumble mess of price action lines. So instead the script averages the data out using 3 different approaches, all selectable in the settings menu.
Geometric Average: useful as it accurately reflects compound returns over time, smoothing out the impact of large gains or losses. Accounts for volatility drift.
Arithmetic Average: a standard average calculation, can be misleading in trading due to volatility drift. It is the most basic form of averaging so I included it.
Median: useful as any big volatility huge moves after a signal does not really impact the mean as it's just the middle value of all values.
These averages are the 2 lines you will find in the middle of the projection. Having a clear difference between a lower break average and upper break average price reaction can signal significance of the trading signal instead of pure chaos.
Outside of this I also included calculations for the maximum and minimum values in the dataset. This is useful for seeing price reactions range to the signal, showing extreme losses or wins are possible. For this range I also included 2 matrices of highs and lows data. This makes it possible to draw a band between the range based on closing price and the one using high/low data.
Below is a visualisation of how the averages data is shown on chart.
⯁ Method 2: Equity Simulation
This method will feel closer to home for traders as it more closely resembles a backtest. It does not include any commissions however and also is just a visualisation of price reaction to a signal. This method will simulate what would happen if you would buy at the breakout point and hold the trade for X amount of bars. With 0 being sell at same bar close. To test robustness I've given the option to visualise Equity simulation not just for 1 simulation but a bunch of simulations.
On default settings it will draw the simulations for 0 bars holding all the way to 10 bars holding. The idea behind it is to check how stable the effect is, to have further confirmation of the significance of the signal. If price simulation line moves up on average for 0 bars all the way to 10 bars holding time that means the signal is steady.
Below is a visualisation of the Equity Simulation.
⯁ Signal filtering
For the boxes themselves where breakouts come from I've included a simple filter based on the size of the box in ATR or %. This will filter out all the boxes that are larger top to bottom than the ATR or % value you setup.
⯁ Coloring of Script
The script includes 5 color themes. There are no color settings or other visual settings in the script, the script themes are simple and always have colors that work well together. Equity simulation uses a gradient based on lightness to color the different lines so it's easier to differentiate them while still upper breaks having a different color than lower breaks.
This script is not created to be used in conjunction with other scripts, it will force you into a background color that matches the theme. It's purpose is a research tool for systematic trading, to analyse signals in more depth.
Metaverse color theme:
⯁ Conclusion
I hope this script will help traders get a deeper understanding of how different assets react to their assets. It should be possible to convert this script into other signals if you know how to code on the platform. It is my intention to make more publications that include this type of analysis. It is especially useful when dealing with signals that do not happen often enough, so a regular backtest is not enough to test their significance. Indicator
Seasonality Monte Carlo Forecaster [BackQuant]Seasonality Monte Carlo Forecaster
Plain-English overview
This tool projects a cone of plausible future prices by combining two ideas that traders already use intuitively: seasonality and uncertainty. It watches how your market typically behaves around this calendar date, turns that seasonal tendency into a small daily “drift,” then runs many randomized price paths forward to estimate where price could land tomorrow, next week, or a month from now. The result is a probability cone with a clear expected path, plus optional overlays that show how past years tended to move from this point on the calendar. It is a planning tool, not a crystal ball: the goal is to quantify ranges and odds so you can size, place stops, set targets, and time entries with more realism.
What Monte Carlo is and why quants rely on it
• Definition . Monte Carlo simulation is a way to answer “what might happen next?” when there is randomness in the system. Instead of producing a single forecast, it generates thousands of alternate futures by repeatedly sampling random shocks and adding them to a model of how prices evolve.
• Why it is used . Markets are noisy. A single point forecast hides risk. Monte Carlo gives a distribution of outcomes so you can reason in probabilities: the median path, the 68% band, the 95% band, tail risks, and the chance of hitting a specific level within a horizon.
• Core strengths in quant finance .
– Path-dependent questions : “What is the probability we touch a stop before a target?” “What is the expected drawdown on the way to my objective?”
– Pricing and risk : Useful for path-dependent options, Value-at-Risk (VaR), expected shortfall (CVaR), stress paths, and scenario analysis when closed-form formulas are unrealistic.
– Planning under uncertainty : Portfolio construction and rebalancing rules can be tested against a cloud of plausible futures rather than a single guess.
• Why it fits trading workflows . It turns gut feel like “seasonality is supportive here” into quantitative ranges: “median path suggests +X% with a 68% band of ±Y%; stop at Z has only ~16% odds of being tagged in N days.”
How this indicator builds its probability cone
1) Seasonal pattern discovery
The script builds two day-of-year maps as new data arrives:
• A return map where each calendar day stores an exponentially smoothed average of that day’s log return (yesterday→today). The smoothing (90% old, 10% new) behaves like an EWMA, letting older seasons matter while adapting to new information.
• A volatility map that tracks the typical absolute return for the same calendar day.
It calculates the day-of-year carefully (with leap-year adjustment) and indexes into a 365-slot seasonal array so “March 18” is compared with past March 18ths. This becomes the seasonal bias that gently nudges simulations up or down on each forecast day.
2) Choice of randomness engine
You can pick how the future shocks are generated:
• Daily mode uses a Gaussian draw with the seasonal bias as the mean and a volatility that comes from realized returns, scaled down to avoid over-fitting. It relies on the Box–Muller transform internally to turn two uniform random numbers into one normal shock.
• Weekly mode uses bootstrap sampling from the seasonal return history (resampling actual historical daily drifts and then blending in a fraction of the seasonal bias). Bootstrapping is robust when the empirical distribution has asymmetry or fatter tails than a normal distribution.
Both modes seed their random draws deterministically per path and day, which makes plots reproducible bar-to-bar and avoids flickering bands.
3) Volatility scaling to current conditions
Markets do not always live in average volatility. The engine computes a simple volatility factor from ATR(20)/price and scales the simulated shocks up or down within sensible bounds (clamped between 0.5× and 2.0×). When the current regime is quiet, the cone narrows; when ranges expand, the cone widens. This prevents the classic mistake of projecting calm markets into a storm or vice versa.
4) Many futures, summarized by percentiles
The model generates a matrix of price paths (capped at 100 runs for performance inside PulseWire), each path stepping forward for your selected horizon. For each forecast day it sorts the simulated prices and pulls key percentiles:
• 5th and 95th → approximate 95% band (outer cone).
• 16th and 84th → approximate 68% band (inner cone).
• 50th → the median or “expected path.”
These are drawn as polylines so you can immediately see central tendency and dispersion.
5) A historical overlay (optional)
Turn on the overlay to sketch a dotted path of what a purely seasonal projection would look like for the next ~30 days using only the return map, no randomness. This is not a forecast; it is a visual reminder of the seasonal drift you are biasing toward.
Inputs you control and how to think about them
Monte Carlo Simulation
• Price Series for Calculation . The source series, typically close.
• Enable Probability Forecasts . Master switch for simulation and drawing.
• Simulation Iterations . Requested number of paths to run. Internally capped at 100 to protect performance, which is generally enough to estimate the percentiles for a trading chart. If you need ultra-smooth bands, shorten the horizon.
• Forecast Days Ahead . The length of the cone. Longer horizons dilute seasonal signal and widen uncertainty.
• Probability Bands . Draw all bands, just 95%, just 68%, or a custom level (display logic remains 68/95 internally; the custom number is for labeling and color choice).
• Pattern Resolution . Daily leans on day-of-year effects like “turn-of-month” or holiday patterns. Weekly biases toward day-of-week tendencies and bootstraps from history.
• Volatility Scaling . On by default so the cone respects today’s range context.
Plotting & UI
• Probability Cone . Plots the outer and inner percentile envelopes.
• Expected Path . Plots the median line through the cone.
• Historical Overlay . Dotted seasonal-only projection for context.
• Band Transparency/Colors . Customize primary (outer) and secondary (inner) band colors and the mean path color. Use higher transparency for cleaner charts.
What appears on your chart
• A cone starting at the most recent bar, fanning outward. The outer lines are the ~95% band; the inner lines are the ~68% band.
• A median path (default blue) running through the center of the cone.
• An info panel on the final historical bar that summarizes simulation count, forecast days, number of seasonal patterns learned, the current day-of-year, expected percentage return to the median, and the approximate 95% half-range in percent.
• Optional historical seasonal path drawn as dotted segments for the next 30 bars.
How to use it in trading
1) Position sizing and stop logic
The cone translates “volatility plus seasonality” into distances.
• Put stops outside the inner band if you want only ~16% odds of a stop-out due to noise before your thesis can play.
• Size positions so that a test of the inner band is survivable and a test of the outer band is rare but acceptable.
• If your target sits inside the 68% band at your horizon, the payoff is likely modest; outside the 68% but inside the 95% can justify “one-good-push” trades; beyond the 95% band is a low-probability flyer—consider scaling plans or optionality.
2) Entry timing with seasonal bias
When the median path slopes up from this calendar date and the cone is relatively narrow, a pullback toward the lower inner band can be a high-quality entry with a tight invalidation. If the median slopes down, fade rallies toward the upper band or step aside if it clashes with your system.
3) Target selection
Project your time horizon to N bars ahead, then pick targets around the median or the opposite inner band depending on your style. You can also anchor dynamic take-profits to the moving median as new bars arrive.
4) Scenario planning & “what-ifs”
Before events, glance at the cone: if the 95% band already spans a huge range, trade smaller, expect whips, and avoid placing stops at obvious band edges. If the cone is unusually tight, consider breakout tactics and be ready to add if volatility expands beyond the inner band with follow-through.
5) Options and vol tactics
• When the cone is tight : Prefer long gamma structures (debit spreads) only if you expect a regime shift; otherwise premium selling may dominate.
• When the cone is wide : Debit structures benefit from range; credit spreads need wider wings or smaller size. Align with your separate IV metrics.
Reading the probability cone like a pro
• Cone slope = seasonal drift. Upward slope means the calendar has historically favored positive drift from this date, downward slope the opposite.
• Cone width = regime volatility. A widening fan tells you that uncertainty grows fast; a narrow cone says the market typically stays contained.
• Mean vs. price gap . If spot trades well above the median path and the upper band, mean-reversion risk is high. If spot presses the lower inner band in an up-sloping cone, you are in the “buy fear” zone.
• Touches and pierces . Touching the inner band is common noise; piercing it with momentum signals potential regime change; the outer band should be rare and often brings snap-backs unless there is a structural catalyst.
Methodological notes (what the code actually does)
• Log returns are used for additivity and better statistical behavior: sim_ret is applied via exp(sim_ret) to evolve price.
• Seasonal arrays are updated online with EWMA (90/10) so the model keeps learning as each bar arrives.
• Leap years are handled; indexing still normalizes into a 365-slot map so the seasonal pattern remains stable.
• Gaussian engine (Daily mode) centers shocks on the seasonal bias with a conservative standard deviation.
• Bootstrap engine (Weekly mode) resamples from observed seasonal returns and adds a fraction of the bias, which captures skew and fat tails better.
• Volatility adjustment multiplies each daily shock by a factor derived from ATR(20)/price, clamped between 0.5 and 2.0 to avoid extreme cones.
• Performance guardrails : simulations are capped at 100 paths; the probability cone uses polylines (no heavy fills) and only draws on the last confirmed bar to keep charts responsive.
• Prerequisite data : at least ~30 seasonal entries are required before the model will draw a cone; otherwise it waits for more history.
Strengths and limitations
• Strengths :
– Probabilistic thinking replaces single-point guessing.
– Seasonality adds a small but meaningful directional bias that many markets exhibit.
– Volatility scaling adapts to the current regime so the cone stays realistic.
• Limitations :
– Seasonality can break around structural changes, policy shifts, or one-off events.
– The number of paths is performance-limited; percentile estimates are good for trading, not for academic precision.
– The model assumes tomorrow’s randomness resembles recent randomness; if regime shifts violently, the cone will lag until the EWMA adapts.
– Holidays and missing sessions can thin the seasonal sample for some assets; be cautious with very short histories.
Tuning guide
• Horizon : 10–20 bars for tactical trades; 30+ for swing planning when you care more about broad ranges than precise targets.
• Iterations : The default 100 is enough for stable 5/16/50/84/95 percentiles. If you crave smoother lines, shorten the horizon or run on higher timeframes.
• Daily vs. Weekly : Daily for equities and crypto where month-end and turn-of-month effects matter; Weekly for futures and FX where day-of-week behavior is strong.
• Volatility scaling : Keep it on. Turn off only when you intentionally want a “pure seasonality” cone unaffected by current turbulence.
Workflow examples
• Swing continuation : Cone slopes up, price pulls into the lower inner band, your system fires. Enter near the band, stop just outside the outer line for the next 3–5 bars, target near the median or the opposite inner band.
• Fade extremes : Cone is flat or down, price gaps to the upper outer band on news, then stalls. Favor mean-reversion toward the median, size small if volatility scaling is elevated.
• Event play : Before CPI or earnings on a proxy index, check cone width. If the inner band is already wide, cut size or prefer options structures that benefit from range.
Good habits
• Pair the cone with your entry engine (breakout, pullback, order flow). Let Monte Carlo do range math; let your system do signal quality.
• Do not anchor blindly to the median; recalc after each bar. When the cone’s slope flips or width jumps, the plan should adapt.
• Validate seasonality for your symbol and timeframe; not every market has strong calendar effects.
Summary
The Seasonality Monte Carlo Forecaster wraps institutional risk planning into a single overlay: a data-driven seasonal drift, realistic volatility scaling, and a probabilistic cone that answers “where could we be, with what odds?” within your trading horizon. Use it to place stops where randomness is less likely to take you out, to set targets aligned with realistic travel, and to size positions with confidence born from distributions rather than hunches. It will not predict the future, but it will keep your decisions anchored to probabilities—the language markets actually speak. Indicator
DCA Simulation for CryptoCommunity v1.1Overview
This script provides a detailed simulation of a Dollar-Cost Averaging (DCA) strategy tailored for crypto traders. It allows users to visualize how their DCA strategy would perform historically under specific parameters. The script is designed to help traders understand the mechanics of DCA and how it influences average price movement, budget utilization, and trade outcomes.
Key Features:
Combines Interval and Safety Order DCA:
Interval DCA: Regular purchases based on predefined time intervals.
Safety Order DCA: Additional buys triggered by percentage price drops.
Interactive Visualization:
Displays buy levels, average price, and profit-taking points on the chart.
Allows traders to assess how their strategy adapts to price movements.
Comprehensive Dashboard:
Tracks money spent, contracts acquired, and budget utilization.
Shows maximum amounts used if profit-taking is active.
Dynamic Safety Orders:
Resets safety orders when a new higher high is established.
Customizable Parameters:
Adjustable buy frequency, safety order settings, and profit-taking levels.
Suitable for traders with varying budgets and risk tolerances.
Default Strategy Settings:
Account Size: Default account size is set to $10,000 to represent a realistic budget for the average trader.
Commission & Slippage: Includes realistic trading fees and slippage assumptions to ensure accurate backtesting results.
Risk Management: Defaults to risking no more than 5% of the account balance per trade.
Sample Size: Optimized to generate a minimum of 100 trades for meaningful statistical analysis. Users can adjust parameters to fit longer timeframes or different datasets.
Usage Instructions:
Configure Your Strategy: Set the base order, safety order size, and buy frequency based on your preferred DCA approach.
Analyze Historical Performance: Use the chart and dashboard to understand how the strategy performs under different market conditions.
Optimize Parameters: Adjust settings to align with your risk tolerance and trading objectives.
Important Notes:
This script is for educational and simulation purposes. It is not intended to provide financial advice or guarantee profitability.
If the strategy's default settings do not meet your needs, feel free to adjust them while keeping risk management in mind.
PulseWire limits the number of open trades to 999, so reduce the buy frequency if necessary to fit longer timeframes.
Strategy
Dual price forecast with Projection Zone [FXSMARTLAB]The Dual Price Forecast with Projection Zone indicator is built to simulate potential future price paths based on historical price movements over two defined lookback periods. By running multiple trials (or simulations) on these historical price movements, the indicator achieves a more robust forecast, incorporating the inherent variability of price behavior.
Key Components and Calculation Details
1. Lookback Periods and Historical Price Movements
Lookback Period 1 and Lookback Period 2 specify the range of past data used to generate each projection. For each period, the indicator calculates the price variations (differences between the closing and opening prices) and stores these in arrays.
These historical price variations capture the volatility and price patterns within each period, serving as templates for future price behavior.
2. Trials: Purpose and Function
The trials are a critical element in the projection calculation. Each trial represents a single simulation of possible future price movements, derived from a random reordering of the historical price variations in each lookback period.
By running multiple trials , the indicator explores various sequences of historical movements, simulating different possible future paths. Each trial adds to the projection’s robustness by capturing a unique potential price path based on past behavior.
Running these multiple trials allows the indicator to account for randomness in price behavior, making the projections more comprehensive by covering a range of scenarios rather than relying on a single deterministic forecast.
3. Reverse Option
The reverse option allows the indicator to invert the direction of price movements within each lookback period. When enabled, historical uptrends are treated as downtrends, and vice versa.
This feature is particularly valuable in scenarios where traders expect a potential reversal in market direction. By enabling the reverse option, the indicator can simulate what might happen if past trends inverted, providing an alternative forecast path that considers possible market reversals.
This allows traders to assess both continuation and reversal scenarios, giving them a more balanced view of potential future price paths and helping them prepare for either market direction.
4. Generating the Average Projection Path
Once the trials are complete, the indicator calculates an average projected price path for each lookback period by averaging the results of all trials. This average represents the most likely price trend based on historical data and provides a smoothed projection that mitigates extreme outliers.
By averaging across all trial paths, the indicator generates a more reliable and balanced forecast line, smoothing out the fluctuations that might appear if only one trial or a small number of trials were used.
5. Projection Zone Visualization
The indicator plots the two average projection paths (one for each lookback period) as Projection 1 and Projection 2, each in a user-defined color.
The Projection Zone is the area between these two lines, filled with a semi-transparent color. This zone visually represents the potential range of future price movement, highlighting where prices are likely to oscillate if historical trends persist.
The Projection Zone effectively functions as a potential support and resistance boundary, providing traders with a visual reference for possible price fluctuations within a specific range.
6. Display of Lookback Zones
To give context to the projections, the indicator can also display colored lookback zones on the chart. These zones correspond to Lookback Period 1 and Lookback Period 2 and are color-coded to match their respective projection lines.
These zones allow traders to see the sections of historical data used in the calculation, helping them understand which past price behaviors influenced the current projections.
Benefits of the Indicator
The "Dual Price Forecast with Projection Zone" indicator provides a multi-scenario forecast based on past price dynamics. Its use of trials ensures that projections are not based on a single deterministic path but on a range of possible scenarios that better reflect the inherent randomness in financial markets.
By generating a probabilistic forecast within a defined zone, the indicator helps traders to:
Anticipate potential price ranges and areas of support/resistance based on historical trends.
Understand the influence of different timeframes (short-term and long-term lookbacks) on future price behavior.
Make informed decisions by visualizing the likely variability of future prices within a controlled projection zone.
Prepare for both continuation and reversal scenarios, thanks to the reverse option. This feature is especially useful in markets where trends may change direction, as it allows traders to explore what might happen
Indicator
Anchored Monte Carlo Shuffled Projection [LuxAlgo]The Anchored Monte Carlo Shuffled Projection tool randomly simulates future price points based on historical bar movements made before a user-anchored point in time.
By anchoring our data and projections to a single point in time, users can better understand and reflect on how the price played out while taking into consideration our random simulations.
🔶 USAGE
After selecting the indicator to apply to the chart, you will be prompted to "Set the Anchor Point". Do so by clicking on the desired location on your chart, only time is used as the anchor point.
Note: To select a new anchor point when applied to the chart, click on the 'More' dropdown next to the indicator status bar (○○○), then select "Reset points...".
Alternate Method: You are also able to click and drag the vertical line that displays on the anchor point bar when the indicator is highlighted.
By randomly simulating bar movements, a range is developed of potential price action which could be utilized to locate future price development as well as potential support/resistance levels.
Performing numerous simulations and taking the average at each step will converge toward the result highlighted by the "Average Line", and can point out where the price might develop, assuming the trend and amount of volatility persist.
Current closing price + Sum of changes in the calculation window
This constraint will cause the simulations always to display an endpoint consistent with the current lookback's slope.
While this may be helpful to some traders, this indicator includes an option to produce a less biased range, as seen below:
🔶 DETAILS
The Anchored Monte Carlo Shuffled Projection tool creates simulations based on prices within a user-set lookback window originating at the specified anchor point. Simulations are done as follows:
Collect each bar's price changes in the user-set window.
Randomize the order of each change in the window.
Project the cumulative sum of the shuffled changes from the current closing price.
Collect data on each point along the way.
This is the process for the Default calculation; for the 'Randomize Direction' calculation, when added onto the front for every other change, the value is inverted, creating the randomized endpoints for each simulation.
The script contains each simulation's data for that bar, with a maximum of 1000 simulations.
To get a glimpse behind the scenes, each simulation (up to 99) can be viewed using the 'Visualize Simulations' Options, as seen below.
Because the script holds the full simulation data, the script can also calculate this data, such as standard deviations.
In this script the Standard deviation lines are the average of all standard deviations across the vertical data groups, this provides a singular value that can be displayed a distance away from the simulation center line.
🔶 SETTINGS
Lookback: Sets the number of Bars to include in calculations.
Simulation Count: Sets the number of randomized simulations to calculate. (Max 1000)
Randomize Direction: See Details Above. Creates a more 'Normalized' Distribution
Visualize Simulations: See Details Above. Turns on Visualizations, and colors are randomly generated. Visualized max does not cap the calculated max. If 1000 simulations are used, the data will be from 1000 simulations, however, only the last 99 simulations will be visualized.
🔹 Standard Deviations
Standard Deviation Multiplier: Sets the multiplier to use for the Standard Deviation distance away from the center line.
🔹 Style
Extend Lines: Extends the Simulated Value Lines into the future for further reference and analysis.
Indicator
Monte Carlo Shuffled Projection [LuxAlgo]The Monte Carlo Shuffled Projection tool randomly simulates future price points based on historical bar movements made within a user-selected window.
The tool shows potential paths price might take in the future, as well as highlighting potential support/resistance levels.
Note that simulations and their resulting elements are subject to slight changes over time.
🔶 USAGE
By randomly simulating bar movements, a range is developed of potential price action which could be utilized to locate future price development as well as potential support/resistance levels.
Performing a large number of simulations and taking the average at each step will converge toward the result highlighted by the "Average Line", and can point out where the price might develop assuming the trend and amount of volatility persist.
Current closing price + Sum of changes in the calculation window)
This constraint will cause the simulations to always display an endpoint consistent with the current lookback's slope.
While this may be helpful to some traders, this indicator includes an option to produce a less biased range as seen below:
🔶 DETAILS
The Monte Carlo Shuffled Projection tool creates simulations based on the most recent prices within a user-set window. Simulations are done as follows:
Collect each bar's price changes in the user-set window.
Randomize the order of each change in the window.
Project the cumulative sum of the shuffled changes from the current closing price.
Collect data on each point along the way.
This is the process for the Default calculation, for the 'Randomize Direction' calculation, when added onto the front for every other change, the value is inverted, creating the randomized endpoints for each simulation.
The script contains each simulation's data for that bar with a maximum of 1000 simulations.
To get a glimpse behind the scenes each simulation (up to 99) can be viewed using the 'Visualize Simulations' Options as seen below.
Because the script holds the full simulation data, the script can also do calculations on this data, such as calculating standard deviations.
In this script the Standard deviation lines are the average of all standard deviations across the vertical data groups, this provides a singular value that can be displayed a distance away from the simulation center line.
🔶 SETTINGS
Color and Toggle Options are Provided throughout.
Lookback: Sets the number of Bars to include in calculations.
Simulation Count: Sets the number of randomized simulations to calculate. (Max 1000)
Randomize Direction: See Details Above. Creates a more 'Normalized' Distribution
Visualize Simulations: See Details Above. Turns on Visualizations, and colors are randomly generated. Visualized max does not cap the calculated max. If 1000 simulations are used, the data will be from 1000 simulations, however only the last 99 simulations will be visualized.
Standard Deviation Multiplier: Sets the multiplier to use for the Standard Deviation distance away from the center line.
Indicator
Indicator
Monte Carlo Range Forecast [DW]This is an experimental study designed to forecast the range of price movement from a specified starting point using a Monte Carlo simulation.
Monte Carlo experiments are a broad class of computational algorithms that utilize random sampling to derive real world numerical results.
These types of algorithms have a number of applications in numerous fields of study including physics, engineering, behavioral sciences, climate forecasting, computer graphics, gaming AI, mathematics, and finance.
Although the applications vary, there is a typical process behind the majority of Monte Carlo methods:
-> First, a distribution of possible inputs is defined.
-> Next, values are generated randomly from the distribution.
-> The values are then fed through some form of deterministic algorithm.
-> And lastly, the results are aggregated over some number of iterations.
In this study, the Monte Carlo process used generates a distribution of aggregate pseudorandom linear price returns summed over a user defined period, then plots standard deviations of the outcomes from the mean outcome generate forecast regions.
The pseudorandom process used in this script relies on a modified Wichmann-Hill pseudorandom number generator (PRNG) algorithm.
Wichmann-Hill is a hybrid generator that uses three linear congruential generators (LCGs) with different prime moduli.
Each LCG within the generator produces an independent, uniformly distributed number between 0 and 1.
The three generated values are then summed and modulo 1 is taken to deliver the final uniformly distributed output.
Because of its long cycle length, Wichmann-Hill is a fantastic generator to use on TV since it's extremely unlikely that you'll ever see a cycle repeat.
The resulting pseudorandom output from this generator has a minimum repetition cycle length of 6,953,607,871,644.
Fun fact: Wichmann-Hill is a widely used PRNG in various software applications. For example, Excel 2003 and later uses this algorithm in its RAND function, and it was the default generator in Python up to v2.2.
The generation algorithm in this script takes the Wichmann-Hill algorithm, and uses a multi-stage transformation process to generate the results.
First, a parent seed is selected. This can either be a fixed value, or a dynamic value.
The dynamic parent value is produced by taking advantage of Pine's timenow variable behavior. It produces a variable parent seed by using a frozen ratio of timenow/time.
Because timenow always reflects the current real time when frozen and the time variable reflects the chart's beginning time when frozen, the ratio of these values produces a new number every time the cache updates.
After a parent seed is selected, its value is then fed through a uniformly distributed seed array generator, which generates multiple arrays of pseudorandom "children" seeds.
The seeds produced in this step are then fed through the main generators to produce arrays of pseudorandom simulated outcomes, and a pseudorandom series to compare with the real series.
The main generators within this script are designed to (at least somewhat) model the stochastic nature of financial time series data.
The first step in this process is to transform the uniform outputs of the Wichmann-Hill into outputs that are normally distributed.
In this script, the transformation is done using an estimate of the normal distribution quantile function.
Quantile functions, otherwise known as percent-point or inverse cumulative distribution functions, specify the value of a random variable such that the probability of the variable being within the value's boundary equals the input probability.
The quantile equation for a normal probability distribution is μ + σ(√2)erf^-1(2(p - 0.5)) where μ is the mean of the distribution, σ is the standard deviation, erf^-1 is the inverse Gauss error function, and p is the probability.
Because erf^-1() does not have a simple, closed form interpretation, it must be approximated.
To keep things lightweight in this approximation, I used a truncated Maclaurin Series expansion for this function with precomputed coefficients and rolled out operations to avoid nested looping.
This method provides a decent approximation of the error function without completely breaking floating point limits or sucking up runtime memory.
Note that there are plenty of more robust techniques to approximate this function, but their memory needs very. I chose this method specifically because of runtime favorability.
To generate a pseudorandom approximately normally distributed variable, the uniformly distributed variable from the Wichmann-Hill algorithm is used as the input probability for the quantile estimator.
Now from here, we get a pretty decent output that could be used itself in the simulation process. Many Monte Carlo simulations and random price generators utilize a normal variable.
However, if you compare the outputs of this normal variable with the actual returns of the real time series, you'll find that the variability in shocks (random changes) doesn't quite behave like it does in real data.
This is because most real financial time series data is more complex. Its distribution may be approximately normal at times, but the variability of its distribution changes over time due to various underlying factors.
In light of this, I believe that returns behave more like a convoluted product distribution rather than just a raw normal.
So the next step to get our procedurally generated returns to more closely emulate the behavior of real returns is to introduce more complexity into our model.
Through experimentation, I've found that a return series more closely emulating real returns can be generated in a three step process:
-> First, generate multiple independent, normally distributed variables simultaneously.
-> Next, apply pseudorandom weighting to each variable ranging from -1 to 1, or some limits within those bounds. This modulates each series to provide more variability in the shocks by producing product distributions.
-> Lastly, add the results together to generate the final pseudorandom output with a convoluted distribution. This adds variable amounts of constructive and destructive interference to produce a more "natural" looking output.
In this script, I use three independent normally distributed variables multiplied by uniform product distributed variables.
The first variable is generated by multiplying a normal variable by one uniformly distributed variable. This produces a bit more tailedness (kurtosis) than a normal distribution, but nothing too extreme.
The second variable is generated by multiplying a normal variable by two uniformly distributed variables. This produces moderately greater tails in the distribution.
The third variable is generated by multiplying a normal variable by three uniformly distributed variables. This produces a distribution with heavier tails.
For additional control of the output distributions, the uniform product distributions are given optional limits.
These limits control the boundaries for the absolute value of the uniform product variables, which affects the tails. In other words, they limit the weighting applied to the normally distributed variables in this transformation.
All three sets are then multiplied by user defined amplitude factors to adjust presence, then added together to produce our final pseudorandom return series with a convoluted product distribution.
Once we have the final, more "natural" looking pseudorandom series, the values are recursively summed over the forecast period to generate a simulated result.
This process of generation, weighting, addition, and summation is repeated over the user defined number of simulations with different seeds generated from the parent to produce our array of initial simulated outcomes.
After the initial simulation array is generated, the max, min, mean and standard deviation of this array are calculated, and the values are stored in holding arrays on each iteration to be called upon later.
Reference difference series and price values are also stored in holding arrays to be used in our comparison plots.
In this script, I use a linear model with simple returns rather than compounding log returns to generate the output.
The reason for this is that in generating outputs this way, we're able to run our simulations recursively from the beginning of the chart, then apply scaling and anchoring post-process.
This allows a greater conservation of runtime memory than the alternative, making it more suitable for doing longer forecasts with heavier amounts of simulations in TV's runtime environment.
From our starting time, the previous bar's price, volatility, and optional drift (expected return) are factored into our holding arrays to generate the final forecast parameters.
After these parameters are computed, the range forecast is produced.
The basis value for the ranges is the mean outcome of the simulations that were run.
Then, quarter standard deviations of the simulated outcomes are added to and subtracted from the basis up to 3σ to generate the forecast ranges.
All of these values are plotted and colorized based on their theoretical probability density. The most likely areas are the warmest colors, and least likely areas are the coolest colors.
An information panel is also displayed at the starting time which shows the starting time and price, forecast type, parent seed value, simulations run, forecast bars, total drift, mean, standard deviation, max outcome, min outcome, and bars remaining.
The interesting thing about simulated outcomes is that although the probability distribution of each simulation is not normal, the distribution of different outcomes converges to a normal one with enough steps.
In light of this, the probability density of outcomes is highest near the initial value + total drift, and decreases the further away from this point you go.
This makes logical sense since the central path is the easiest one to travel.
Given the ever changing state of markets, I find this tool to be best suited for shorter term forecasts.
However, if the movements of price are expected to remain relatively stable, longer term forecasts may be equally as valid.
There are many possible ways for users to apply this tool to their analysis setups. For example, the forecast ranges may be used as a guide to help users set risk targets.
Or, the generated levels could be used in conjunction with other indicators for meaningful confluence signals.
More advanced users could even extrapolate the functions used within this script for various purposes, such as generating pseudorandom data to test systems on, perform integration and approximations, etc.
These are just a few examples of potential uses of this script. How you choose to use it to benefit your trading, analysis, and coding is entirely up to you.
If nothing else, I think this is a pretty neat script simply for the novelty of it.
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How To Use:
When you first add the script to your chart, you will be prompted to confirm the starting date and time, number of bars to forecast, number of simulations to run, and whether to include drift assumption.
You will also be prompted to confirm the forecast type. There are two types to choose from:
-> End Result - This uses the values from the end of the simulation throughout the forecast interval.
-> Developing - This uses the values that develop from bar to bar, providing a real-time outlook.
You can always update these settings after confirmation as well.
Once these inputs are confirmed, the script will boot up and automatically generate the forecast in a separate pane.
Note that if there is no bar of data at the time you wish to start the forecast, the script will automatically detect use the next available bar after the specified start time.
From here, you can now control the rest of the settings.
The "Seeding Settings" section controls the initial seed value used to generate the children that produce the simulations.
In this section, you can control whether the seed is a fixed value, or a dynamic one.
Since selecting the dynamic parent option will change the seed value every time you change the settings or refresh your chart, there is a "Regenerate" input built into the script.
This input is a dummy input that isn't connected to any of the calculations. The purpose of this input is to force an update of the dynamic parent without affecting the generator or forecast settings.
Note that because we're running a limited number of simulations, different parent seeds will typically yield slightly different forecast ranges.
When using a small number of simulations, you will likely see a higher amount of variance between differently seeded results because smaller numbers of sampled simulations yield a heavier bias.
The more simulations you run, the smaller this variance will become since the outcomes become more convergent toward the same distribution, so the differences between differently seeded forecasts will become more marginal.
When using a dynamic parent, pay attention to the dispersion of ranges.
When you find a set of ranges that is dispersed how you like with your configuration, set your fixed parent value to the parent seed that shows in the info panel.
This will allow you to replicate that dispersion behavior again in the future.
An important thing to note when settings alerts on the plotted levels, or using them as components for signals in other scripts, is to decide on a fixed value for your parent seed to avoid minor repainting due to seed changes.
When the parent seed is fixed, no repainting occurs.
The "Amplitude Settings" section controls the amplitude coefficients for the three differently tailed generators.
These amplitude factors will change the difference series output for each simulation by controlling how aggressively each series moves.
When "Adjust Amplitude Coefficients" is disabled, all three coefficients are set to 1.
Note that if you expect volatility to significantly diverge from its historical values over the forecast interval, try experimenting with these factors to match your anticipation.
The "Weighting Settings" section controls the weighting boundaries for the three generators.
These weighting limits affect how tailed the distributions in each generator are, which in turn affects the final series outputs.
The maximum absolute value range for the weights is . When "Limit Generator Weights" is disabled, this is the range that is automatically used.
The last set of inputs is the "Display Settings", where you can control the visual outputs.
From here, you can select to display either "Forecast" or "Difference Comparison" via the "Output Display Type" dropdown tab.
"Forecast" is the type displayed by default. This plots the end result or developing forecast ranges.
There is an option with this display type to show the developing extremes of the simulations. This option is enabled by default.
There's also an option with this display type to show one of the simulated price series from the set alongside actual prices.
This allows you to visually compare simulated prices alongside the real prices.
"Difference Comparison" allows you to visually compare a synthetic difference series from the set alongside the actual difference series.
This display method is primarily useful for visually tuning the amplitude and weighting settings of the generators.
There are also info panel settings on the bottom, which allow you to control size, colors, and date format for the panel.
It's all pretty simple to use once you get the hang of it. So play around with the settings and see what kinds of forecasts you can generate!
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ADDITIONAL NOTES & DISCLAIMERS
Although I've done a number of things within this script to keep runtime demands as low as possible, the fact remains that this script is fairly computationally heavy.
Because of this, you may get random timeouts when using this script.
This could be due to either random drops in available runtime on the server, using too many simulations, or running the simulations over too many bars.
If it's just a random drop in runtime on the server, hide and unhide the script, re-add it to the chart, or simply refresh the page.
If the timeout persists after trying this, then you'll need to adjust your settings to a less demanding configuration.
Please note that no specific claims are being made in regards to this script's predictive accuracy.
It must be understood that this model is based on randomized price generation with assumed constant drift and dispersion from historical data before the starting point.
Models like these not consider the real world factors that may influence price movement (economic changes, seasonality, macro-trends, instrument hype, etc.), nor the changes in sample distribution that may occur.
In light of this, it's perfectly possible for price data to exceed even the most extreme simulated outcomes.
The future is uncertain, and becomes increasingly uncertain with each passing point in time.
Predictive models of any type can vary significantly in performance at any point in time, and nobody can guarantee any specific type of future performance.
When using forecasts in making decisions, DO NOT treat them as any form of guarantee that values will fall within the predicted range.
When basing your trading decisions on any trading methodology or utility, predictive or not, you do so at your own risk.
No guarantee is being issued regarding the accuracy of this forecast model.
Forecasting is very far from an exact science, and the results from any forecast are designed to be interpreted as potential outcomes rather than anything concrete.
With that being said, when applied prudently and treated as "general case scenarios", forecast models like these may very well be potentially beneficial tools to have in the arsenal. Indicator
Particle Physics Moving AverageThis indicator simulates the physics of a particle attracted by a distance-dependent force towards the evolving value of the series it's applied to.
Its parameters include:
The mass of the particle
The exponent of the force function f=d^x
A "medium damping factor" (viscosity of the universe)
Compression/extension damping factors (for simulating spring-damping functions)
This implementation also adds a second set of all of these parameters, and tracks 16 particles evenly interpolated between the two sets.
It's a kind of Swiss Army Knife of Moving Average-type functions; For instance, because the position and velocity of the particle include a "historical knowlege" of the series, it turns out that the Exponential Moving Average function simply "falls out" of the algorithm in certain configurations; instead of being configured by defining a period of samples over which to calculate an Exponential Moving Average, in this derivation, it is tuned by changing the mass and/or medium damping parameters.
But the algorithm can do much more than simply replicate an EMA... A particle acted on by a force that is a linear function of distance (force exponent=1) simulates the physics of a sprung-mass system, with a mass-dependent resonant frequency. By altering the particle mass and damping parameters, you can simulate something like an automobile suspension, letting your particle track a stock's price like a Cadillac or a Corvette (or both, including intermediates) depending on your setup. Particles will have a natural resonance with a frequency that depends on its mass... A higher mass particle (i.e. higher inertia) will resonate at a lower frequency than one with a lower mass (and of course, in this indicator, you can display particles that interpolate through a range of masses.)
The real beauty of this general-purpose algorithm is that the force function can be extended with other components, affecting the trajectory of the particle; For instance "volume" could be factored into the current distance-based force function, strengthening or weakening the impulse accordingly. (I'll probably provide updates to the script that incoroprate different ideas I come up with.)
As currently pictured above, the indicator is interpolating between a medium-damped EMA-like configuration (red) and a more extension-damped suspension-like configuration (blue).
This indicator is merely a tool that provides a space to explore such a simulation, to let you see how tweaking parameters affects the simulations. It doesn't provide buy or sell signals, although you might find that it could be adapted into an MACD-like signal generator... But you're on your own for that. Indicator
