
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: 27 
Joined: Jul 2018 


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). 



Thanks. Is there any rule of thumb regarding window size? 
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doomanx


Total Posts: 27 
Joined: Jul 2018 


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 relearning along with your model each time. 



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: 1157 
Joined: Jun 2007 


This is very hard to answer without a more exact description of how you measure "explainatory" power. I hope we are not talking adjusted RSquared 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 autofit 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.rproject.org/web/packages/forecast/forecast.pdf http://pkg.robjhyndman.com/forecast/

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lass lieber deine Fäuste sprechen...



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. 

