Diggle, P.J. 　著

内容

目次

Part 1 Introduction: definitions and notation; objectives oftime-series analysis; more notation; trend, serial dependence andstationarity; 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 onautocorrelation structure; the periodogram; the connection between thecorrelogram 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 andaccumulation of stationary random functions; implications ofautocorrelation for elementary statistical methods. Part 4 Spectralanalysis: the periodogram revisited; periodogram-based tests of whitenoise; the fast Fournier transform; periodogram averages; other smoothestimates of the spectrum; adjusting spectral estimates for the effectsof filtering; combining and comparing spectral estimates; fittingparametric models; strengths and weaknesses of spectral analysis. Part5 Repeated measurements: repeated measurements as multivariate data;incorporating time-series structure; formulating the model - time-plotsand the variogram; fitting the model - analysis of data on proteincontent of milk samples. Part 6 Fitting autoregressive moving averageprocesses to data: ARIMA processes as models for non-stationarytime-series; identification; estimation; diagnostic checking;case-studies. Part 7 Forecasting: preamble; forecasting byextrapolation of polynomial trends; exponential smoothing; theBox-Jenkins approach to forecasting. Part 8 Elements of bivariatetime-series analysis: the cross-covariance and cross-correlationfunctions; estimating the cross-correlation function; the spectrum of abivariate process; estimating the cross-spectrum.