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ATR BandsIt has happened to everybody. You enter the market, the position gets a stop loss, then later the market goes in the direction you originally planned. Worse yet - you enter a position, the market goes in your favor, gets near the target, and then it reverses and you get stopped.
We brazilians call this a "violinado", or getting violinated. It happens either because:
1. You put the stop loss too close, or the target too far
2. You entered in the right direction, but at a wrong time
While the second point cannot be programmly adressed, the first can. One popular way of setting a stop loss is by using the average of the true range, it even has a built-in indicator in TV. The problem with it is that you can still get violinated, since as the trend develops, the stop loss only goes up, never down. So if you enter at the wrong time, one slip can still take you out of the market.
Since I got sick of losing money using a conventional stop loss, I made these ATR bands. When you add this indicator to your graph, 6 lines are going to show up, 3 above the price, 3 below it. These lines are calculated from the ATR of the last 20 periods (can be configurated). The upper lines are the high of the last candle + the ATR * the multiplicator factor, the lower lines are the low - ATR * multiplicator factor. There are three multiplicator factors: 1.0, 1.618 and 2.0, and you change them to be whatever you want.
The logic behind it is that theses bands represents the region in which the market is more likely to stay. So if you enter the market at 50.00, you can't expect it to reach 500.00 in the next hour if the ATR is 5.00. And if you set the stop loss at 49.99, it is very likely that the market is going to stop you. By using the ATR bands, you can get a more reasonable price range, so you would set the stop loss at 45.00 and the take profit level at 60.00.
There are two types os ATR you can use: the regular, calculated with RMA, and another using a custom WMA, which puts greater emphasis on large amplitudes. By default, the average uses the past 20 true ranges. You can also choose to use either the closing price or the extremes of the candle as a basis.
Another thing I've added is the violation statistics, which shows the percentages of the times that a band was violated in the next 5 candles (can be configurated). With this, you can get a broader view on the probability of the bands actually being reached.
You may have notice that the bands are lagged by 1 period. I did this so that there is no way you can use future data. You can disable it or increase it, but I recommend just letting it be 1. These bands are the range in which the price is most likely to stay in, if you change the lag you are essentially breaking it's whole purpose. Indicator

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Square Root Moving AverageAbstract
This script computes moving averages which the weighting of the recent quarter takes up about a half weight.
This script also provides their upper bands and lower bands.
You can apply moving average or band strategies with this script.
Introduction
Moving average is a popular indicator which can eliminate market noise and observe trend.
There are several moving average related strategies used by many traders.
The first one is trade when the price is far from moving average.
To measure if the price is far from moving average, traders may need a lower band and an upper band.
Bollinger bands use standard derivation and Keltner channels use average true range.
In up trend, moving average and lower band can be support.
In ranging market, lower band can be support and upper band can be resistance.
In down trend, moving average and upper band can be resistance.
An another group of moving average strategy is comparing short term moving average and long term moving average.
Moving average cross, Awesome oscillators and MACD belong to this group.
The period and weightings of moving averages are also topics.
Period, as known as length, means how many days are computed by moving averages.
Weighting means how much weight the price of a day takes up in moving averages.
For simple moving averages, the weightings of each day are equal.
For most of non-simple moving averages, the weightings of more recent days are higher than the weightings of less recent days.
Many trading courses say the concept of trading strategies is more important than the settings of moving averages.
However, we can observe some characteristics of price movement to design the weightings of moving averages and make them more meaningful.
In this research, we use the observation that when there are no significant events, when the time frame becomes 4 times, the average true range becomes about 2 times.
For example, the average true range in 4-hour chart is about 2 times of the average true range in 1-hour chart; the average true range in 1-hour chart is about 2 times of the average true range in 15-minute chart.
Therefore, the goal of design is making the weighting of the most recent quarter is close to the weighting of the rest recent three quarters.
For example, for the 24-day moving average, the weighting of the most recent 6 days is close to the weighting of the rest 18 days.
Computing the weighting
The formula of moving average is
sum ( price of day n * weighting of day n ) / sum ( weighting of day n )
Day 1 is the most recent day and day k+1 is the day before day k.
For more convenient explanation, we don't expect sum ( weighting of day n ) is equal to 1.
To make the weighting of the most recent quarter is close to the weighting of the rest recent three quarters, we have
sum ( weighting of day 4n ) = 2 * sum ( weighting of day n )
If when weighting of day 1 is 1, we have
sum ( weighting of day n ) = sqrt ( n )
weighting of day n = sqrt ( n ) - sqrt ( n-1 )
weighting of day 2 ≒ 1.414 - 1.000 = 0.414
weighting of day 3 ≒ 1.732 - 1.414 = 0.318
weighting of day 4 ≒ 2.000 - 1.732 = 0.268
If we follow this formula, the weighting of day 1 is too strong and the moving average may be not stable.
To reduce the weighting of day 1 and keep the spirit of the formula, we can add a parameter (we call it as x_1w2b).
The formula becomes
weighting of day n = sqrt ( n+x_1w2b ) - sqrt ( n-1+x_1w2b )
if x_1w2b is 0.25, then we have
weighting of day 1 = sqrt(1.25) - sqrt(0.25) ≒ 1.1 - 0.5 = 0.6
weighting of day 2 = sqrt(2.25) - sqrt(1.25) ≒ 1.5 - 1.1 = 0.4
weighting of day 3 = sqrt(3.25) - sqrt(2.25) ≒ 1.8 - 1.5 = 0.3
weighting of day 4 = sqrt(4.25) - sqrt(3.25) ≒ 2.06 - 1.8 = 0.26
weighting of day 5 = sqrt(5.25) - sqrt(4.25) ≒ 2.3 - 2.06 = 0.24
weighting of day 6 = sqrt(6.25) - sqrt(5.25) ≒ 2.5 - 2.3 = 0.2
weighting of day 7 = sqrt(7.25) - sqrt(6.25) ≒ 2.7 - 2.5 = 0.2
What you see and can adjust in this script
This script plots three moving averages described above.
The short term one is default magenta, 6 days and 1 atr.
The middle term one is default yellow, 24 days and 2 atr.
The long term one is default green, 96 days and 4 atr.
I arrange the short term 6 days to make it close to sma(5).
The other twos are arranged according to 4x length and 2x atr.
There are 9 curves plotted by this script. I made the lower bands and the upper bands less clear than moving averages so it is less possible misrecognizing lower or upper bands as moving averages.
x_src : how to compute the reference price of a day, using 1 to 4 of open, high, low and close.
len : how many days are computed by moving averages
atr : how many days are computed by average true range
multi : the distance from the moving average to the lower band and the distance from the moving average to the lower band are equal to multi * average true range.
x_1w2b : adjust this number to avoid the weighting of day 1 from being too strong.
Conclusion
There are moving averages which the weighting of the most recent quarter is close to the weighting of the rest recent three quarters.
We can apply strategies based on moving averages. Like most of indicators, oversold does not always means it is an opportunity to buy.
If the short term lower band is close to the middle term moving average or the middle term lower band is close to the long term moving average, it may be potential support value.
References
Computing FIR Filters Using Arrays
How to trade with moving averages : the eight trading signals concluded by Granville
How to trade with Bollinger bands
How to trade with double Bollinger bands Indicator

Resampling Reverse Engineering Bands [DW]This is an experimental study designed to reverse engineer price levels from centered oscillators at user defined sample rates.
This study aims to educate users on the process of oscillator reverse engineering, and to give users an alternative perspective on some of the most commonly used oscillators in the trading game.
Reverse engineering price levels from an oscillator is actually a rather simple, straightforward process.
Rather than plugging price values into a function to solve for oscillator values, we rearrange the function using some basic algebraic operations and plug in a specified oscillator value to solve for price values instead.
This process tells us what price value is needed in order for the oscillator to equal a certain value.
For example, if you wanted to know what price value would be considered “overbought” or “oversold” according to your oscillator, you can do that using this process.
In this study, the reverse engineering functions are used to calculate the price values of user defined high and low oscillator thresholds, and the price values for the oscillator center.
This allows you to visualize what prices will trigger thresholds as a sort of confidence interval, which is information that isn't inherently available when simply analyzing the oscillator directly.
This script is equipped with three reverse engineering functions to choose from for calculating the band values:
-> Reverse Relative Strength Index (RRSI)
-> Reverse Stochastic Oscillator (RStoch)
-> Reverse Commodity Channel Index (RCCI)
You can easily select the function you want to utilize from the "Band Calculation Type" dropdown tab.
These functions are specially designed to calculate at any sample rate (up to 1 bar per sample) utilizing the process of downsampling that I introduced in my Resampling Filter Pack.
The sample rate can be determined with any of these three methods:
-> BPS - Resamples based on the number of bars.
-> Interval - Resamples based on time in multiples of current charting timeframe.
-> PA - Resamples based on changes in price action by a specified size. The PA algorithm in this script is derived from my Range Filter algorithm.
The range for PA method can be sized in points, pips, ticks, % of price, ATR, average change, and absolute quantity.
Utilizing downsampled rates allows you to visualize the reverse engineered values of an oscillator calculated at larger sample scales.
This can be rather beneficial for trend analysis since lower sample rates completely remove certain levels of noise.
By default, the sample rate is set to 1 BPS, which is the same as bar-to-bar calculation. Feel free to experiment with the sample rate parameters and configure them how you like.
Custom bar colors are included as well. The color scheme is based on disparity between sources and the reverse engineered center level.
In addition, background highlights are included to indicate when price is outside the bands, thus indicating "overbought" and "oversold" conditions according to the thresholds you set.
I also included four external output variables for easy integration of signals with other scripts:
-> Trend Signals (Current Resolution Prices) - Outputs 1 for bullish and -1 for bearish based on disparity between current resolution source and the central level output.
-> Trend Signals (Resampled Prices) - Outputs 1 for bullish and -1 for bearish based on disparity between resampled source and the central level output.
-> Outside Band Signal (Current Resolution Prices) - Outputs 1 for overbought and -1 for oversold based on current resolution source being outside the bands. Returns 0 otherwise.
-> Outside Band Signal (Resampled Prices) - Outputs 1 for overbought and -1 for oversold based on resampled source being outside the bands. Returns 0 otherwise.
To use these signals with another script, simply select the corresponding external output you want to use from your script's source input dropdown tab.
Reverse engineering oscillators is a simple, yet powerful approach to incorporate into your momentum or trend analysis setup.
By incorporating projected price levels from oscillators into our analysis setups, we are able to gain valuable insights, make (potentially) smarter trading decisions, and visualize the oscillators we know and love in a totally different way.
I hope you all find this script useful and enjoyable! Indicator

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Combo Backtest 123 Reversal & Fractal Chaos Bands This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
Stock market moves in a highly chaotic way, but at a larger scale, the movements
follow a certain pattern that can be applied to shorter or longer periods of time
and we can use Fractal Chaos Bands Indicator to identify those patterns. Basically,
the Fractal Chaos Bands Indicator helps us to identify whether the stock market is
trending or not. When a market is trending, the bands will have a slope and if market
is not trending the bands will flatten out. As the slope of the bands decreases, it
signifies that the market is choppy, insecure and variable. As the graph becomes more
and more abrupt, be it going up or down, the significance is that the market becomes
trendy, or stable. Fractal Chaos Bands Indicator is used similarly to other bands-indicator
(Bollinger bands for instance), offering trading opportunities when price moves above or
under the fractal lines.
The FCB indicator looks back in time depending on the number of time periods trader selected
to plot the indicator. The upper fractal line is made by plotting stock price highs and the
lower fractal line is made by plotting stock price lows. Essentially, the Fractal Chaos Bands
show an overall panorama of the price movement, as they filter out the insignificant fluctuations
of the stock price.
WARNING:
- For purpose educate only
- This script to change bars colors. Strategy

Combo Strategy 123 Reversal & Fractal Chaos Bands This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
Stock market moves in a highly chaotic way, but at a larger scale, the movements
follow a certain pattern that can be applied to shorter or longer periods of time
and we can use Fractal Chaos Bands Indicator to identify those patterns. Basically,
the Fractal Chaos Bands Indicator helps us to identify whether the stock market is
trending or not. When a market is trending, the bands will have a slope and if market
is not trending the bands will flatten out. As the slope of the bands decreases, it
signifies that the market is choppy, insecure and variable. As the graph becomes more
and more abrupt, be it going up or down, the significance is that the market becomes
trendy, or stable. Fractal Chaos Bands Indicator is used similarly to other bands-indicator
(Bollinger bands for instance), offering trading opportunities when price moves above or
under the fractal lines.
The FCB indicator looks back in time depending on the number of time periods trader selected
to plot the indicator. The upper fractal line is made by plotting stock price highs and the
lower fractal line is made by plotting stock price lows. Essentially, the Fractal Chaos Bands
show an overall panorama of the price movement, as they filter out the insignificant fluctuations
of the stock price.
WARNING:
- For purpose educate only
- This script to change bars colors. Indicator

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