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trialanderror


Total Posts: 34
Joined: Feb 2019
 
Posted: 2019-09-25 18:11
I have a question regarding regression analysis of expected return on asset prices. I know from econometrics classes that you should transform prices into returns to get stationary processes to regress on before trying to model the process. Are there other types of transformations that are better or somehow useful?

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doomanx


Total Posts: 35
Joined: Jul 2018
 
Posted: 2019-09-25 20:10
Filtering is a useful transformation for reducing the noise in raw price data. You may have heard of the simple (yet very effective) moving average filter. This is very helpful as fitting a model to smoothed data will resist 'fitting the noise' (joining up the dots) and hence provide a more robust fit (in ML literature one would call it reducing variance at the cost of a hopefully small amount of bias).

trialanderror


Total Posts: 34
Joined: Feb 2019
 
Posted: 2019-09-26 07:39
Thanks. Is there any rule of thumb regarding window size?

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doomanx


Total Posts: 35
Joined: Jul 2018
 
Posted: 2019-09-26 08:32
Unfortunately not. The window size is how you control the memory of your process. It is a hyperparameter and hence comes with all the usual problems of choosing hyperparameters in a robust/sensible way. It may not even be stationary and hence require re-learning along with your model each time.

trialanderror


Total Posts: 34
Joined: Feb 2019
 
Posted: 2019-09-26 09:09
I see. Suppose I just want to try out the approach on some data and I randomly pick a window size of 10. If it does not look like there is any explanatory power in the model, is it relatively safe to conclude that no window size is going to achieve good results or is it important to conduct for example a grid search in all cases to be sure?

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Maggette


Total Posts: 1167
Joined: Jun 2007
 
Posted: 2019-09-26 17:48
This is very hard to answer without a more exact description of how you measure "explainatory" power. I hope we are not talking adjusted R-Squared here or something like that.

Window length for smoothing/filtering in time series means selecting a hyperparameter or a set of hyperparameters. Hence all the techniques to avoid overfitting also apply here.

There are a lot filtering/smoothing techniques available, moving averages and exponential moving averages are just two of them.

So I am afraid nobody can give an decent answer here without a better understanding what you are trying to achieve.

Regards
Mag

edit: for forecasting you could have a look at Hyndmans forecasting package in R and the ETS model family, which are a family of additive and multiplicative exponential smoothing models (like Hold Winters).

ETS is an auto-fit function that tries to select the right model for you (and hence that includes fitting the anologon of the window length), by maximizing the R**2 or std of the residuals (all in sample).

Please don't expect anything useful for raw financial returns data though!!!


https://cran.r-project.org/web/packages/forecast/forecast.pdf
http://pkg.robjhyndman.com/forecast/

Ich kam hierher und sah dich und deine Leute lächeln, und sagte mir: Maggette, scheiss auf den small talk, lass lieber deine Fäuste sprechen...

trialanderror


Total Posts: 34
Joined: Feb 2019
 
Posted: 2019-09-27 15:12
Thanks for your answer @maggette, I realise that my question was deeper than I thought when I wrote it. I'll take your advice with me and post another question with something more specific when I can.

Regards

Nous promettons selon nos espérances, et nous tenons selon nos craintes.
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