Exercises

  1. ARMA Model Fitting

    • Use the detrended and seasonally adjusted time series from exercise 2 from chapter Decomposing Time Series. Fit an AR(1), MA(1), ARMA(1,1) and ARMA(2,2) model to the data using ML estimation. Choose the best out of these four approaches using the Akaike Information Criteria.

  2. Forecasting

    • Predict the values of the detrended and seasonally - adjusted retailers sales time series for the next six months (for the next 12 months) using the best model from exercise 1.

  3. Causality and Invertibility (Homework)

    • Check if the best model from exercise 1 is causal w.r.t \(\epsilon\) by using the polyroot() function.
    • Check if the best model from exercise 1 is invertible w.r.t \(\epsilon\) by using the polyroot() function.
    • Note: More about causality and invertibility of \(ARMA(p,q)\) processes can be found here