Reversion To the Mean (RTM) Intraday Strategies

[Frank Thomas]

Just my .02:

But what I think Maestro is talking about is using numerical analysis to curve fit a function (polynomial function and maybe even a Transcendental function) to the data and then building a distribution of the deviations from the function (which I think if the curve fit is done correctly) that will follow a normal distribution or another distribution that allows him to calculate the probability accurately enough in order to fade the movement of the market with the expectation of the price reverting back to the value of the function (which is changing with every trade). The challenge of doing this I think is trying to figure out how to curve fit the function.

 

[knocks420]

My .02

The challenge isn't in finding a better method to fit prices, its finding a security or transformation of securities that fit a MR process.

 

[ivanbaj]

Quote from knocks420:

My .02

The challenge isn't in finding a better method to fit prices, its finding a security or transformation of securities that fit a MR process.

I agree. I eyeball it.

 

[IronFist]

MAESTRO already suggested that his "mean" is not a MA.

My questions to MAESTRO are:

1) what are you using as your mean?

2) how do you know when price is about to revert? Is it a function of its distance from the mean?

3) does your RTM strategy involve averaging down?

 

[dtrader98]

Quote from ASusilovic:

Higher degree polynoms ? Stuff like this :


f(x) = a0xn + a1xn-1 + a2xn-2 + ... + an

The equation above is not a higher degree polynomial.

The MA is a low pass filter, not a high pass filter. Simple differencing of consecutive series elements (detrending) is one way to generate a crude high pass filter.

I can't speak for Maestro, but (regarding model fitting) if I want to get a nice smooth general model fit with minimal idiosyncratic noise, I'll take a spline type fit over a moving average any day.

 

[Humpy]

Quote from dtrader98:

The equation above is not a higher degree polynomial.

The MA is a low pass filter, not a high pass filter. Simple differencing of consecutive series elements (detrending) is one way to generate a crude high pass filter.

I can't speak for Maestro, but (regarding model fitting) if I want to get a nice smooth general model fit with minimal idiosyncratic noise, I'll take a spline type fit over a moving average any day.

Nice looking curve from spline fit dtrader98

Care to share the formula here ? (preferably for Metastock )

 

[knocks420]

Quote from dtrader98:

The equation above is not a higher degree polynomial.

The MA is a low pass filter, not a high pass filter. Simple differencing of consecutive series elements (detrending) is one way to generate a crude high pass filter.

I can't speak for Maestro, but (regarding model fitting) if I want to get a nice smooth general model fit with minimal idiosyncratic noise, I'll take a spline type fit over a moving average any day.

Spline looks interesting from the chart but I have to ask how you decided to compare against an MA(10). Its quite possible that various look-back periods will result in different PDFs. By optimizing one can find an MA that matches a Normal Dist. and a Spline that deviates from it. Perhaps though you have run tests to check for robustness?

Additionally your still stuck with in essence a non-stationary series so the data/rules of the game are changing on you.

 

[goldenarm]

The morning OPG basket orders is the only reversion to the mean strategy that I've seen work.

 

[MAESTRO]

Quote from dtrader98:

The equation above is not a higher degree polynomial.

The MA is a low pass filter, not a high pass filter. Simple differencing of consecutive series elements (detrending) is one way to generate a crude high pass filter.

I can't speak for Maestro, but (regarding model fitting) if I want to get a nice smooth general model fit with minimal idiosyncratic noise, I'll take a spline type fit over a moving average any day.

Right on the money, dtrader98! cubic spline interpolations is the family of curves that GUARANTEE Gaussian distribution around each point! Congratulations! Very good! Now, the challenge is to design a practical algorithm to exploit this phenomenon and you have your Holy Grail!

 

[MAESTRO]

Quote from Fractals 'R Us:

I think he's referring to some math that got developed fairly recently wherein somehow, and don't ask me how, they can somewhat predict the next data point in a series of data.. I looked into it once, part of it went over my head and the rest of it went way over my head... can't recall what it was called though but mathematically speaking... and I'm no mathematician, but nonetheless, it is predicting the future and we tend to think that's technically impossible but of course there are always really smart guys and gals tucked away inside some university somewhere doing the impossible... One guy can get a Nobel Prize for proving that it's impossible and another can get a Nobel Prize for doing it... maybe some really hip person can tell us what that branch of math is... I could find it if I had to, it was posted on ET years ago, but I'm not going to that trouble today...

Very warm, almost there!