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Characteristics of Time Series
Spectral Analysis and Filtering
9 other sections not shown
ANOPOW applied approximate ARIMA ARIMA model assumed autocorrelation function autocovariance function autoregressive model autoregressive process Brillinger Chapter CM CM CM coefficients components computed consider correlation covariance matrix cross covariance cycles per point defined degrees of freedom denotes detrended discriminant function earthquake equation example explosions F statistic forecast Fourier transform frequency domain Frequency in cycles frequency response frequency response function given impulse response function Input number input series linear filter log likelihood mean-square error mortality moving average multivariate normal noise process noise series normal distribution number of series observed PACF parameters partial autocorrelation peaks periodic periodogram plotted power spectrum prediction problem procedure random variables recursions regression model residuals result Rx(m sample Section series analysis shown in Figure shows Shumway signal smoothed spectral analysis spectral estimator state-space model stationary process stationary time series Table temperature theoretical variance vector wave number white noise zero zero-mean