ZLMA - Low-Lag Moving Average Based On An Alternative SMA Design

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There 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.


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).


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.
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@alexgrover, very interesting technique -- let me PM you my comment on it.
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your strategy help me earn much money , you are super genius
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Well done, congrats again!
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@Zekis, Thx
Very interesting, nice work Alex! I'll publish a trend-colored phase-cross strategy made from this if anyone wants. You can compare two different lag values to determine the trend.
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alexgrover jaggedsoft
@jaggedsoft, Sorry but i won't allow it, as i don't judge it being a meaningful change, are you only aware of the rules? And you have been doing that for quite some time now, take time to read them
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jaggedsoft alexgrover
I did not mean any offense, I'm one of your top fans and just sharing my observations. I always appreciated comments from others letting me know my work was being used or discussed. For you I'll keep quiet. Be well
alexgrover jaggedsoft
@jaggedsoft, Its not about keeping quiet or anything, its not only about me either, i'am more than open to work with others or let them use my scripts as long as they properly ask for it, but we have to know the rules in order for the community to be healthy, when i add work to the moderation team i feel extremely guilty. If you judge that i'am being mean then i'll tell you that i could just wait for you to post your "trend-colored phase-cross strategy" and ask the mods to remove it, and you would get banned.
jaggedsoft alexgrover
@alexgrover, why would I copy your phase cross? mine has less lag than yours ;) 3m chart:

your scripts are licensed for public use and modification. what exactly is your problem? I admire you a great deal but you should chill and take it as a compliment. If it makes you feel better my most liked script is a derivative of yours. G-Channel is your best work to date but most don't realize it. My derivative of your G-Channel got over 5 times the likes compared to yours because I applied it for trend analysis which is a different application than what you intended, and added features making it practical for people to use. I hope you find happiness, I enjoy the things you create a great deal and you should too. Be kind to people, don't threaten others when we're all just trying to sharpen our skills and become better at our craft and what we're passionate about. I don't care about views or likes or my free tradingview account. I'm only here to make money. I wish you all the best, you are truly impressive and your potential has no bounds. Thanks for the inspiration. You won't be hearing anything further from me.
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