Time Series

Part 1 Introduction: definitions and notation; objectives of time-series analysis; more notation; trend, serial dependence and stationarity; duality between trend and serial dependence; software. Part 2 Simple descriptive methods of analysis: time-plots; smoothing; differencing; the autocovariance and autocorrelation functions; estimating the autocorrelation function; impact of trend-removal on autocorrelation structure; the periodogram; the connection between the correlogram and the periodogram. Part 3 Theory of stationary processes: notation and definitions; the spectrum of a stationary random process; linear filters; the autoregressive moving average process; sampling and accumulation of stationary random functions; implications of autocorrelation for elementary statistical methods. Part 4 Spectral analysis: the periodogram revisited; periodogram-based tests of white noise; the fast Fournier transform; periodogram averages; other smooth estimates of the spectrum; adjusting spectral estimates for the effects of filtering; combining and comparing spectral estimates; fitting parametric models; strengths and weaknesses of spectral analysis. Part 5 Repeated measurements: repeated measurements as multivariate data; incorporating time-series structure; formulating the model - time-plots and the variogram; fitting the model - analysis of data on protein content of milk samples. Part 6 Fitting autoregressive moving average processes to data: ARIMA processes as models for non-stationary time-series; identification; estimation; diagnostic checking; case-studies. Part 7 Forecasting: preamble; forecasting by extrapolation of polynomial trends; exponential smoothing; the Box-Jenkins approach to forecasting. Part 8 Elements of bivariate time-series analysis: the cross-covariance and cross-correlation functions; estimating the cross-correlation function; the spectrum of a bivariate process; estimating the cross-spectrum.