By Daniel Peña; George C Tiao; Ruey S Tsay
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Extra resources for A course in time series analysis
And Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco. Box, G. E. , Jenkins, G. M. and Reinsel, G. (1994). Time Series Analysis: Forecasting and Control, 3rd ed. Prentice-Hall, Englewood Cliffs, NJ. Box, G. E. P. and Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. J. Am. Stat. Assoc. 75, 70-79. Box, G. E. P. and Tiao, G. C. (1977). A canonical analysis of multiple time series. Biometirka 64,355-366.
Furthermore, because A — Β — 0, the distribution of the periodogram at such frequencies is a scaled chi-squared variable on 2 degrees of freedom, also known as an exponential 2 0 distribution: 1(f) = ^ ( A + Β) ~ σ χ 2 2 2 2 2 = exponential^ ). 36) These properties are exact if the frequencies of the cycles are exact multiples j of the harmonic frequency 1/n, that is, if they have an exact number j of cycles in the data length. The cyclical regressors are then mutually orthogonal, and the estimates at these frequencies are independent.
The sample autocorrelation function (acf) provides a widely used statistical summary of the properties of an observed times series. 5 contains four frames in the first of which a plot of the first 100 values of the steel consumption time series is shown, and in the second its sample autocorrelations. The remaining two frames show the sample partial autocorrelation function and sample spectral density, which will be described shortly. Note how the sample autocorrelation in this case summarizes the cyclical properties of the series with peaks at lags 4 and 16 indicating the periods of the cycles.
A course in time series analysis by Daniel Peña; George C Tiao; Ruey S Tsay