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:

$$\mbox{return}(t+1) = a + bf + e.$$

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!

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!