Course information

This course provides a comprehensive introduction to the statistical analysis and forecasting of time-dependent data. It begins with the fundamental concepts of time series, its components, and additive and multiplicative models, followed by methods for estimating and removing trend and seasonal effects using moving averages and exponential smoothing techniques. Simple Exponential Smoothing, Holt’s and Holt-Winters’ methods are studied for forecasting. The course then introduces time series as discrete-parameter stochastic processes, with emphasis on autocovariance, autocorrelation, partial autocorrelation, and stationarity. The Wold representation and Box–Jenkins models, including AR, MA, ARMA, and ARIMA, are examined in detail. Parameter estimation using Yule-Walker, least squares, and maximum likelihood methods, model selection, MMSE forecasting, residual analysis, and diagnostic checking are covered. The course also introduces spectral analysis, periodograms, spectral density of ARMA processes, seasonal ARIMA models, and ARCH and GARCH models, providing a foundation for advanced time series modelling and forecasting.