Rolling price returns in a linear regression

Question

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!

Answer 1

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.