This course introduces students to the statistical basis behind model identification, model fitting and model criticism of time series probability models in both time and frequency domains.

Components of a time series; smoothing methods; trend projection; deseasonalising a time series, autocorrelation; autoregressive models; integrated models; estimation in the time domain; the Box-Jenkins approach; spectral analysis, the spectral distribution function, the spectral density function, Fourier analysis, periodogram analysis, the fast Fourier transform; forecasting methods, extrapolation, Holt-Winters, Box-Jenkins, prediction theory; bivariate processes, the cross-correlation function, the cross-spectrum; applied time series analysis using suitable software packages.

* Calculate theoretical autocorrelation function, partial autocorrelation function, spectrum and spectral density of autoregressive integrated moving average stationary time series models. * Use the sample autocorrelation function, sample partial autocorrelation function, cumulative periodogram, and time series diagnostic plots for a set of data to identify a suitable model in the seasonal autoregressive integrated moving average family of time series models * Calculate and use model fitting and parameter estimation methods and criteria such as maximum likelihood estimation, Yule-Walker equations, AkaikeÆs information criterion and SchwartzÆs Bayesian information criterion * Calculate forecasts and the appropriate forecast prediction error for seasonal autoregressive integrated moving average time series models * Calculate the cross- autocorrelation function, cross-partial autocorrelation function, and cross-spectrum for bivariate time series models * Compute and interpret computer output from the statistical software packages R for time series analysis of real data

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Computer laboratories and tutorials