4.4 Forecasting

• One of the main practical uses of time series models is for forecasting future observations
• The existence of time dependence in a covariance stationary time series means that we can exploit this time dependence to obtain forecasts of future observations that are superior to the unconditional mean.
• Describe basic forecasting problem
• Show result that conditional mean is optimal mse forecast
• Show chain-rule of forecasting for AR(1) processes