1LC-LSMA (1 line code lsma with 3 functions)

Even Shorter Estimation

I know that i'am insistent with the lsma but i really like it and i'm happy to deconstruct it like a mad pinescript user. But if you have an idea about some kind of indicator then dont hesitate to contact me, i would be happy to help you if its feasible.

My motivation for such indicator was to use back the correlation function (that i had putted aside in the ligh-lsma code) and provide a shorter code than the estimation using the line rescaling method (see : Approximating A Least Square Moving Average In Pine).

The Method

Fairly simple, lets name y our estimation, we calculate it as follow:

y = x̄ + r*o*1.7

where x̄ is the price moving average, r the correlation between the price and a line (or n) and o the standard deviation. If plotted against a classic lsma the difference would be meaningless at first glance so lets plot the absolute value between the difference of the lsma and our estimation of both period 100.



The difference is under 0.0000 on eurusd, its really low.

In general the longer the period of the estimation, the lower the difference between a normal lsma, but when using shorter period they can differ a little bit.

Why 1.7 ?

We need to multiply the standard deviation by a constant in order to match the overshoot and the rise-time of the original lsma. The constant 1.7 is one that work well but actually this constant should be dependant of the length period of the filter to make the estimation more accurate.



More About Step-Response

Most of the time when a filter have less lag, it mean that he induce overshoot in order to decrease the rise-time. Rise-time is the time the output take to match the target input, its related to the lag. Overshoot mean that the output exceed the target input, you can clearly see those concept in the image above.

Conclusion

I've showed that its possible to be even more concise about the code it take to estimate an lsma. I've also briefly explained the concept of rise-time and overshoot, concepts really important to signal processing and particularly in filter design. I'm sure that it can be even more simplified and i have some ideas for such estimate.

Thanks for reading !