Degeneration of an ARMA or MA model over time

[WWD]

Course: AI and Machine Learning Specialist

Module: Forecasting and Optimization Specialist

Submodule: Forecasting using Model Studio using SAS Viya

When dealing with Time-Series forecasting using a model that contains a moving-average term, what does SAS do when predicting future values and there are no actual values to difference from the predicted values for the MA term?  Because the moving-average term uses some form of the difference between an actual value and predicted value, eventually, if enough predictions are made, there will be no actual values.  

My question is: If an ARMA model is fit to the data and we've made enough future predictions to run out of historic actual values, does the original ARMA model used for predictions degenerate into a AR model?

If a moving-average model is fit to the data, do future predictions eventually degenerate into the series mean?

Thank you,

Bill Donaldson

[HarrySnart]

Hi, I think your question may be a more general point around how an ARIMA(p,d,q) model works. With any predictive/statistical model the task is learning the pattern from training data, the validation data is used to ensure the model generalises well to new observations. The difference to Data Mining in Time Series is that the train/validation split is based on time indexed observations and the validation component is typically the most recent known observations for a representative sample size. The ARIMA model learns appropriate parameters for p,d,q which are the AR, Integration and MA components of the model. When making a prediction with an ARIMA model it is generating new values based on the known AR and MA lags. The integration step transforms the data into a stationary series so that data fluctuates around a static mean, i.e. an ARMA model is learned from the stationary series. When predicting new values these are done using the learned MA and AR parameters around the stationary mean of the series. The model stability will generally decay the further you get from the last known values in the series with an N-step forecast. This is further complicated by other factors such as exogenous variables or seasonality in the data. I hope this answers your questions. Thanks, Harry    

[WWD]

Thank you for helping me out.

Bill Donaldson