Stat Sept 2008 D. R. Brillinger Chapter 5 - Forecasting Data x 1,..., x N What about x N+h, h>0 No single method universally applicable extrapolation conditional statement scenarios

Conditional expected value, E(Y|X) X can be vector-valued Y = X N+h X=(X 1,...,X N )

Multiple regression Fit by least squares lm() Residuals

Linear c's to minimize E(X N+h - c 0 X N -...-c N-1 X 1 ) 2 Conditional expected value if {X t } Gaussian/normal

Prediction/forecast error Linear process The error is Represent series as linear process

Box-Jenkins Model. arima(p,d,q) Stages of Box-Jenkins forecasting model (1) Model identification. Which p,d,q? (2) Estimation. arima() (3) Diagnostic checking. residuals (4) Consideration of alternate models. If necessary Cp. The scientific method

Pertinent R functions arima() tsdiag() predict() - applied to output of arima help("predict.Arima")