NY Times 23 Sept time series of the day

Stat Sept 2008 D. R. Brillinger Chapter 4 - Fitting t.s. models in the time domain sample autocovariance coefficient. Under stationarity,...

Estimated autocorrelation coefficient asymptotically normal interpretation

Uses of acf mixing (asymptotically independent)? MA(q)? Seasonal component? ergodic

Estimating the mean Can be bigger or less than  2 /N

Fitting an autoregressive, AR(p) Easy. Remember regression and least squares normal equations

AR(1) Cp.

Fitting an MA(q). Later. There is an R program Fitting an ARMA(p,q). Later. There is an R program Estimating p, q, (p,q). Later. There is a criterion.

Seasonal ARIMA. seasonal parameter s SARIMA(p,d,q)  (P,D,Q) s Example

Residual analysis. Paradigm observation = fitted value plus residual The parametric models have contained Z t

Plot residuals vs. t Acf of residuals

Portmanteau lack-of-fit statistic ARMA(p,q) appropriate?

Model building (1) model formulation (2) model estimation (3) model checking All models are wrong but some are useful