Relative slopeRelative slope metric
Description:
I was in need to create a simple, naive and elegant metric that was able to tell how strong is the trend in a given rolling window. While abstaining from using more complicated and arguably more precise approaches, I’ve decided to use Linearly Weighted Linear Regression slope for this goal. Outright values are useful, but the problem was that I wasn’t able to use it in comparative analysis, i.e between different assets & different resolutions & different window sizes, because obviously the outputs are scale-variant.
Here is the asset-agnostic, resolution-agnostic and window size agnostic version of the metric.
I made it asset agnostic & resolution agnostic by including spread information to the formula. In our case it's weighted stdev over differenced data (otherwise we contaminate the spread with the trend info). And I made it window size agnostic by adding a non-linear relation of length to the output, so finally it will be aprox in (-1, 1) interval, by taking square root of length, nothing fancy. All these / 2 and * 2 in unexpected places all around the formula help us to return the data to it’s natural scale while keeping the transformations in place.
Peace TV
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Weighted Standard Deviation BandsLinearly weighted standard deviations over linearly weighted mean.
The rationale of the study can be deduced from my latest publications where I go deeper into explaining the benefits of linear weighting, but in short, I can remind that by using linear weighting we are able to increase the information gain by communicating the sequential nature of time series to the calculations via linear weighting.
Note, that multiplier parameters can take both negative and positive values resulting in ability to have, for example, 1st and 6th weighted standard deviations higher than the weighted mean.
Despite the modification of the classic standard deviation formula, I assume that mathematical qualities of standard deviation will hold due to the fact we can alternately weight the window itself, and then apply the classic standard deviation over the weighted window. In both cases, the results will be the same.
Aight that was too formal, but your short strangles should be happy
Here is it, for you Indicator
StrengthA mathematically elegant, native & modern way how to measure velocity/ strength/ momentum. As you can see it looks like MACD, but !suddenly! has N times shorter code (disregard the functions), and only 1 parameter instead of 3. OMG HOW DID HE DO IT?!?
MACD: "Let's take one filter (1 parameter), than another filter (2 parameters), then let's take dem difference, then let's place another filter over the difference (3rd parameter + introduction of a nested calculation), and let's write a whole book about it, make thousands of multi-hours YouTube videos about it, and let's never mention about the amount of uncertainty being introduced by multiple parameters & introduction of the nested calculation."
Strength: "let's get real, let's drop a weighted linear regression & usual linear regression over the data of the same length, take dem slopes, then make the difference over these slopes, all good. And then share it with people w/o putting an ® sign".
Fyi, regressions were introduced centuries ago, maybe decades idk, the point is long time ago, and computational power enough to calculate what I'm saying is slightly more than required for macd.
Rationale.
Linearly weighted linear regression has steeper slope (W) than the usual linear regression slope (S) due to the fact that the recent datapoints got more weight. This alone is enough of a metric to measure velocity. But still I've recalled macd and decided to make smth like it cuz I knew it'll might make you happy. I realized that S can be used instead of smoothing the W, thus eliminating the nested calculation and keeping entropy & info loss in place. And see, what we get is natural, simple, makes sense and brings flex. I also wanna remind you that by applying regression we maximize the info gain by using all the data in the window, instead of taking difference between the first and the last datapoints.
This script is dedicated to my friend Fabien. Man, you were the light in the darkness in that company. You'll get your alien green Lambo if you'll really want it, no doubts on my side bout that.
Good hunting Indicator
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Weighted Least Squares Moving AverageLinearly Weighted Ordinary Least Squares Moving Regression
aka Weighted Least Squares Moving Average -> WLSMA
^^ called it this way just to for... damn, forgot the word
Totally pwns LSMA for some purposes here's why (just look up):
- 'realistically' the same smoothness;
- less lag;
- less overshoot;
- more or less same computationally intensive.
"Pretty cool, huh?", Bucky Roberts©, thenewboston
Now, would you please (just look down) and see the comparison of impulse & step responses:
Impulse responses
Step responses
Ain't it beautiful?
"Motivation behind the concept & rationale", by gorx1
Many been trippin' applying stats methods that require normally distributed data to time series, hence all these B*ll**** Bands and stuff don't really work as it should, while people blame themselves and buy snake oil seminars bout trading psychology, instead of using proper tools. Price... Neither population nor the samples are neither normally nor log-normally distributed. So we can't use all the stuff if we wanna get better results. I'm not talking bout passing each rolling window to a stat test in order to get the proper descriptor, that's the whole different story.
Instead we can leverage the fact that our data is time-series hence we can apply linear weighting, basically we extract another info component from the data and use it to get better results. Volume, range weighting don't make much sense (saying that based on both common sense and test results). Tick count per bar, that would be nice tho... this is the way to measure "intensity". But we don't have it on TV unfortunately.
Anyways, I'm both unhappy that no1 dropped it before me during all these years so I gotta do it myself, and happy that I can give smth cool to every1
Here is it, for you.
P.S.: the script contains standalone functions to calculate linearly weighted variance, linearly weighted standard deviation, linearly weighted covariance and linearly weighted correlation.
Good hunting Indicator
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LWMA: Linear Weighted Moving AverageCouldn't find searching for Linearly Weighted Moving Average (LWMA) in pulsewire. Found one with the LWMA title, but it uses plain WMA calculation without the linearity which more heavily weights recent price data, which I need, so I try to made one.
LWMAs are also quicker to react to price changes than SMA and EMA. If you want a moving average with less lag than an SMA, try a LWMA.
It kind of also have a more clarity in defining the price trend and reversals. Trade signals usually based on crossovers, they can also indicate areas of potential support or resistance. But beware though, multiple false signals may also occur before a significant trend develops. Use a filter, some decent volatility oscillator might do the job.
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The formula for this Linearly Weighted Moving Average is:
LWMA = (( P n∗ W 1)+( P n−1∗ W 2)+( P n−2∗ W 3)...) / ∑W
P = Price for the period
n = The most recent period, n-1 is the prior period, and n-2 is two periods prior
W = The assigned weight to each period, with the highest weight going first and then descending linearly based on the number of periods being used.
I hope I'm doing right translating it to Pine Script 4. Let me know if I miss something.
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