# time series with rolling returns using periodicreturns

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azim on 19 Oct 2018
Commented: azim on 7 Nov 2018
i was working on some financial data on matlab and using it for time series forecasting. there is a function in it periodicreturns(TotalReturnPrices,Period). if i choose a period of say 5 days it gives me rolling return periodic values with period 5. so for example i have prices like [100, 110, 120, 130, 120, 110, 100, 90, 95, 100, 105, 107, 100, 110, 108] so using the above function i get the returns as following: 1) (120-100)/100 = 0.20; 2) (110-110)/110=0; 3) (100-120)/120=0.1667 etc... so i have around 10 rolling returns like this. now if i had say 1000 daily prices and i calculate rolling returns with period of say one month (around 26 days) and i have 974 such kind of rolling returns. can i use these returns for time series model estimation (arima, arima-garch etc) and forecasting? will using these kind of rolling returns introduce any kind of stationarity issues, co-integration errors etc? i'am a novice in time series so i don't have the slightest clue of errors using spurious data. but i just thought using rolling returns are we using overlapping data or data too close to each other. your help in this matter would be highly obliged. thanks azim

Hang Qian on 7 Nov 2018
Yes, you can use these returns for time series model estimation (arima, arima-garch etc) and forecasting. If the daily return is stationary (which is usually true for asset return data), then the rolling-window returns remain stationary, provided that the rolling-window size is fixed. I do not think spurious data or co-integration errors are issues for rolling regressions. However, the rolling returns have some serial correlation, due to the overlapping periods. ARIMA models in the Econometrics Toolbox can take care of such correlation.
Hang Qian
azim on 7 Nov 2018
Hi hang Thanks for the great explanation. Yeah I have fixed the rolling window size to 26 days for one problem and calculated one arma-garch model and another arma-gjr garch model. Now I will just check again for serial correlation of the data ( which you said the toolbox will take care of itself). Thanks for the help. IAM much obliged. Regards Azim