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I want to conduct a linear regression (in matlab) using rolling monthly returns; the aim is to give me a prediction for the next monthly rolling period return.

return calculation:

$$\mbox{return}(t) = \dfrac{\mbox{Price}(t) - \mbox{Price}(t-30)}{\mbox{Price}(t-30)}.$$

regression:

$$\mbox{return}(t+1) = a + b_1f_1 + b_2f_2 +b_3f_3+ e.$$

My question is what is the best way to conduct a linear regression using a rolling return with a time horizon greater than $1$ day?

Thanks!

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    $\begingroup$ I find significant autocorrelation in the residuals from calculating the rolling return in such a method $\endgroup$
    – user1129988
    Commented Jul 3, 2012 at 11:50

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Build an ARIMA model that captures the effect of memory and level shifts/time trends,seasonal pulses and one time pulses. Make sure that you accomodate/detect changes in parameters and changes in variance over time. Use that equation to forecast prixes and then convert the forecast price to a return. If you have possible predictor series incorporate them into the model thus generalizing to a TRansfer Function. If you wish to post the historical prices I will try and help you.

Additional comment: As you suggested there are possible supporting/causal/input/exogenous series thus a Transfer Function would be appropriate.

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  • $\begingroup$ I cant post the prices here because the file is to big but this link to historical prices is a suitable substitute: finance.yahoo.com/q/… $\endgroup$
    – user1129988
    Commented Jul 3, 2012 at 12:51
  • $\begingroup$ how will the ARIMA handle the rolling return calculation, do I just use the same specification in matlab for the linear regression.. stats = regstats(X,y,'linear') but instead use the ARIMA function? $\endgroup$
    – user1129988
    Commented Jul 3, 2012 at 12:53
  • $\begingroup$ I edited the original post.. there are also factors with in the model such as price to book and market cap $\endgroup$
    – user1129988
    Commented Jul 3, 2012 at 13:08
  • $\begingroup$ Could you point me to any literature that has more detail on the process? thanks! $\endgroup$
    – user1129988
    Commented Jul 4, 2012 at 6:41
  • $\begingroup$ When it comes to stock returns, time-trends, seasonality and the like are more likely to be an artefact of any in sample dataset you are working with and would not likely generalise. $\endgroup$
    – Jase
    Commented Oct 15, 2013 at 6:30

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