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Submitted By skips247msughter
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TIME SERIES
Contents
Syllabus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Models for time series 1.1 Time series data . . . . . . . . . . . . . 1.2 Trend, seasonality, cycles and residuals 1.3 Stationary processes . . . . . . . . . . 1.4 Autoregressive processes . . . . . . . . 1.5 Moving average processes . . . . . . . . 1.6 White noise . . . . . . . . . . . . . . . 1.7 The turning point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii iii iv 1 1 1 1 2 3 4 4 5 5 5 6 6 7 7 8 9 9 9 12 13 13 15 16 17 17 17 18 19

2 Models of stationary processes 2.1 Purely indeterministic processes . . . . . . 2.2 ARMA processes . . . . . . . . . . . . . . 2.3 ARIMA processes . . . . . . . . . . . . . . 2.4 Estimation of the autocovariance function 2.5 Identifying a MA(q) process . . . . . . . . 2.6 Identifying an AR(p) process . . . . . . . . 2.7 Distributions of the ACF and PACF . . .

3 Spectral methods 3.1 The discrete Fourier transform . . . . . . . . . . . . . . . . . . . . . . 3.2 The spectral density . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Analysing the effects of smoothing . . . . . . . . . . . . . . . . . . . . 4 Estimation of the spectrum 4.1 The periodogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Distribution of spectral estimates . . . . . . .

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