ARIMA model forecasting out-of-sample

[Joshua Adams]

Hello all,

I would appreciate if somebody could advice on the best approach to forecast time series (out-of-sample) using ARIMA. My data has 528 observations, mean (-.0016047) and st. dev (1.282545). I have conducted initial tests and through logging and first differencing I made sure that the data is stationary (has a mean reversal property), there is no serial correlation and also cleaned my sample from the outliers. With help of the partial autocorrelation correlogram, I identified the optimal lagged terms to run the ARIMA regression and ended up with “arima lna, arima(6,1,2)”.

Questions:

1. Please advice on the commands in STATA to help me forecast the time series for period T+1 using the aforementioned ARIMA model with 95% and 99% confidence level bands.
2. How would you recommend an overall approach to back-test the accuracy of the model using the historical data? In other words, how can I see that my ARIMA predictions fit the actual historical data.
3. At last, please recommend on the intuitive interpretation of the AIC and BIC for choosing the right model. Should I choose the model that has the lowest value of AIC or BIC.

Thank you so much in advance for your input. I would really appreciate it.

Kind regards,

Joshua

[Alvaro Fuentes]

Joshua, before you go an try to do forecasting with your model, notice that neither of the MA terms are significant. I think you probably:

- Saw that the partial correlogram suggested 6 AR terms
- Saw that the autocorrelogram suggested 2 MA terms
- Decided to fit an ARMA(6,2)

That's wrong. You should either use the AR(6) suggestion OR the MA(2) suggestion, NOT BOTH.

After fitting the AR(6), you can check if the residuals of the model still have something MA to be modelled (which I doubt because the 6 ARs probably pick up all the dynamics). Only then would you want to fit an ARMA.
OR
After fitting the MA(2), you can check if the residuals of the model still have something AR to be modelled. Only then would you want to fit an ARMA.

[Joshua Adams]

Hello Alvaro, thank you for pointing it out. I will make the modifications to the model and try to see how it fits. If you or somebody else on the forum can answer the aforementioned questions, I would appreciate it.