REVERSED RESIDUALS IN AUTOREGRESSIVE TIME SERIES ANALYSIS |
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| Authors: | A. J. Lawrance P. A. W. Lewis |
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| Affiliation: | University of Birmingham and Naval Postgraduate School, Monterey |
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| Abstract: | Abstract. Both linear and non-linear time series can have directional features which can be used to enhance the modelling and investigation of linear or non-linear autoregressive statistical models. For this purpose, reversed p th-order residuals are introduced. Cross-correlations of residuals and squared reversed residuals allow extensions of current model identification ideas. Quadratic types of partial autocorrelation functions are introduced to assess dependence associated with non-linear models which nevertheless have linear autoregressive correlation structures. The use of these residuals and their cross-correlation functions is exemplified empirically on some deseasonalized river flow data for which a first-order autoregressive model is a satisfactory second-order fit. Parallel theoretical computations are undertaken for the non-linear first-order random coefficient autoregressive model and comparisons are made. While the data are shown to be strongly non-linear, their correlational signatures are found to be convincingly different from those of a first-order autoregressive model with random coefficients. |
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| Keywords: | Autoregression autoregressive time series analysis autoregressive models directionality non-linearity ordinary residuals random coefficient autoregressive models residuals reversed pth-order autoregressive residuals reversed residuals reversibility squared residuals squared reverse residuals time series |
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