By Daniel Peña; George C Tiao; Ruey S Tsay
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Extra info for A course in time series analysis
The first step is to correct both the regressor z, and the new predictor z , - for the effects of the current predictor Z(-i by forming ζ, —φι,ιζ,_ι and ζ , _ — φι,ιζ,_ι. The coefficient φι,ι is the same in both of these because both z, and z , _ have the same autocorrelation with, and hence the same dependence upon, z,_i. The partial autocorrelation at lag 2 is just the correlation between these corrected terms. 4. 22) from which, by comparing coefficients, we see that Φ2,ι = φι,ι — φ2,2φι,ι· This computation generalizes to provide an efficient means of solving the Yule-Walker equations which has been historically important.
Among them are long memory processes (Beran 1994), wavelets (Hardle et al. 1998, Morettin 1999), and discrimination and clustering in time series (Karizawa et al. 1998). REFERENCES Abraham, B. and Ledolter, J. (1983). Statistical Methods for Forecasting. Wiley, New York. Anderson, B. O. and Moore, J. B. (1979). Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ. Anderson, T. W. (1971). The Statistical Analysis of Time Series. Springer-Verlag, New York. Aoki, M. (1990). State Space Modeling of Time Series.
It is sometimes appropriate to take logarithms of the values of a time series before embarking on any other analysis. This can help to improve the fit of a linear model UNIVARIATE TIME SERIES 36 before regression or other modeling of the series. Other such instantaneous nonlinear transformations, such as taking the square root, can be useful for improving the linear modeling of stationary series. Differencing of a time series is a simple operation that can often transform a nonstationary time series to a stationary series.
A course in time series analysis by Daniel Peña; George C Tiao; Ruey S Tsay