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ZLMA - Low-Lag Moving Average Based On An Alternative SMA DesignThere can be many ways to make a simple moving average, you can either sum the current and the n-1 previous data points and divide the result by n , or you can do it more efficiently by first taking the cumulative sum of your data points, and subtracting the current cumulative sum result with the cumulative sum results n bars ago, then divide the result by n . This can be described by the following formulas:
a(t) = a(t-1) + price(t)
b(t) = (a(t) - a(t-n))/n
This method is the one used in order to allow the user to use a series as SMA period, more info here:
Today we use this design in order to provide a pretty efficient low-lag moving average where the amount of lag of the moving average can be increased/decreased by the user.
THE INDICATOR
length control the period of the moving average, with larger value of length returning larger filtering amount. The lag setting in the other hand control the amount of lag of the moving average, with larger value of lag returning a moving average with less lag. The lag setting can't be lower than 1 or greater than 2, but values lower than 1 and greater than 0 would just return a moving average with larger filtering amount while values greater than 2 would create crazy wild overshoots.
In blue lag = 1.8, in red lag = 1.4, when lag = 1 the moving average is equal to a simple moving average of period length. Remember that larger values of lag will return greater over/undershoots.
Approximate amplitude response of the moving average, like all low-lag moving averages you can see frequencies amplified (the ones on the left greater than 1) .
SUMMARY
We proposed a low-lag moving average based on the cumulative/change SMA design where the lag of the moving average can be controlled by the user. There are tons of low-lag moving averages already, and they don't necessarily provide different results from each others, however this one is still relatively interesting as you can switch from a simple MA from a low-lagging one, other indicators are ready using this design and will be posted soon. Indicator
Moving Averages Linear CombinatorLinearly combining moving averages can provide relatively interesting results such as a low-lagging moving averages or moving averages able to produce more pertinent crosses with the price.
As a remainder, a linear combination is a mathematical expression that is based on the multiplication of two variables (or terms) with two coefficients (also called scalars when working with vectors) and adding the results, that is:
ax + by
This expression is a linear combination , with x/y as variables and a/b as coefficients. Lot of indicators are made from linear combinations of moving averages, some examples include the double/triple exponential moving average, least squares moving average and the hull moving average.
Today proposed indicator allow the user to combine many types of moving averages together in order to get different results, we will introduce each settings of the indicator as well as how they affect the final output.
Explaining The Effects Of Linear Combinations
There are various ways to explain why linear combination can produce low-lagging moving averages, lets take for example the linear combination of a fast SMA of period p/2 and slow simple moving average of period p , the linear combination of these two moving averages is described as follows:
MA = 2SMA(p/2) + -1SMA(p)
Which is equivalent to:
MA = 2SMA(p/2) - SMA(p) = SMA(p/2) + SMA(p/2) - SMA(p)
We can see the above linear combinations consist in adding a bandpass filter to the fast moving average, which of course allow to reduce the lag. It is important to note that lag is reduced when the first moving average term is more reactive than the second moving average term. In case we instead use:
MA = -2SMA(p/2) + 1SMA(p)
we would have a combination between a low-pass and band-reject filter.
The Indicator
The indicator is based on the following linear combination:
Coeff × LeadingMA(length) - (Coeff-1) × LaggingMA(length)
The length setting control both moving averages period, leading control the type of moving average used as leading MA, while lagging control the type of MA used as lagging moving average, in order to get low lag results the leading MA should be more reactive than the lagging MA. Coeff control the coefficients of the linear combination, with higher values of coeff amplifying the effects of the linear combination, negative values of coeff would make a low-lag moving average become a lagging moving average, coeff = 1 return the leading MA, coeff = -1 return the lagging MA. The leading period divisor allow to divide the period of the leading MA by the selected number.
The types of moving average available are: simple, exponentially weighted, triangular, least squares, hull and volume weighted. The lagging MA allow you to select another MA on the chart as input.
length = 100, leading period divisor = 2, coeff = 2, with both MA type = SMA. Using coeff = -2 instead would give:
You can select "Plot leading and lagging" in order to show the leading and lagging MA.
Conclusion
The proposed tool allow the user to create a custom moving averages by making use of linear combination. The script is not that useful when you think about it, and might maybe be one of my worst, as it is relatively impractical, not proud of it, but it still took time to make so i decided to post it anyway.
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[fikira] Fibonacci MA / EMA's (Fibma / Fibema)I've made SMA/EMA's NOT based on the principle of the 2(1+1), 3(2+1),
5(3+2), 8(5+3), 13(8+5), 21(13+8), 34(21+13), 55(34+21), ... numbers,
but based on these following Fibonacci numbers:
0,236
0,382
0,500
0,618
0,764
1
Ending up with 2 series of Fibma / Fibema:
"Tiny Fibma / Fibema":
24, 38, 50, 62, 76, 100
"Big Fibma / Fibema":
236, 382, 500, 618, 764, 1000
IMHO it is striking how these lines often act as Resistance/Support,
although (except the 50, 100 & 500) they are not typical MA/EMA's.
They perform very well on every Timeframe as well!
Week:
3 Days:
1 Day:
4h:
1h:
Even on the 15 minutes:
Or 5':
Things to watch for:
Price compared to the Tiny or Big Fibma / Fibema (below or above)
Price compared to important Fibma / Fibema (for example below or
above MA 236, MA 764, MA 1000, ...)
Crossing of Fibma / Fibema 24/76, 236/764 and 38/62, 382/618
(bullish crossover = Lime coloured "cloud", bearish crossunder = Red coloured "cloud"),
...
I've made a change in barcolor if the close crosses the "Big Fibma / Fibema 500"
If price closes above MA/EMA 500, the first bar is yellow coloured,
if price stays above this level, candles are coloured lime/orange (= very bullish)
If price closes under MA/EMA 500, the first bar is purple,
if price stays under this level, candles are standard coloured (= very bearish)
Strategy will follow,
Thanks!
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Functions Allowing Series As Length - PineCoders FAQ█ WARNING
Improvements to the following Pine built-ins have deprecated the vast majority of this publication's functions, as the built-ins now accept "series int" `length` arguments:
ta.wma()
ta.linreg()
ta.variance()
ta.stdev()
ta.correlation()
NOTE
For an EMA function that allows a "series int" argument for `length`, please see `ema2()` in the ta library by PulseWire .
█ ORIGINAL DESCRIPTION
Pinescript requires many of its built-in functions to use a simple int as their period length, which entails the period length cannot vary during the script's execution. These functions allow using a series int or series float for their period length, which means it can vary on each bar.
The functions shared in this script include:
Rolling sum: Sum(src,p)
Simple moving average: Sma(src,p)
Rolling variance: Variance(src,p)
Rolling standard deviation: Stdev(src,p)
Rolling covariance: Covariance(x,y,p)
Rolling correlation: Correlation(x,y,p)
If p is a float then it is rounded to the nearest int .
How to Use the Script
Most of the functions in the script are dependent on the Sma function. The Correlation function uses the Covariance and Stdev functions. Be sure you include all the required functions in your script.
Make sure the series you use as the length argument is greater than 0, else the functions will return na . When using a series as length argument, the following error might appear:
Pine cannot determine the referencing length of a series. Try using max_bars_back in the study or strategy function.
This can be frequent if you use barssince(condition) where condition is a relatively rare event. You can fix it by including max_bars_back=5000 in your study declaration statement as follows:
study("Title",overlay=true,max_bars_back=5000)
Example
The chart shows the Sma , Stdev , Covariance and Correlation functions. The Sma uses the closing price as input and bars as period length where:
bars = barssince(change(security(syminfo.tickerid,"D",close ,lookahead=true)))
The Stdev uses the closing price as input and bars + 9 as period length. The Covariance and Correlation use the closing price as x and bar_index as y , with bars + 9 as period length.
Look first. Then leap.
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