Modelling and residual analysis of nonlinear auto-regressive time series in exponential variables
Lewis, Peter A. W.
Lawrance, A. J.
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An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by analysis of a long series of wind velocity data which has first been detrended and then transformed into a stationary series with an exponential marginal distribution. The stationary series is modelled with a newly developed type of second order autoregressive process with random coefficients, called the NEAR(2) model; it has a second order autoregressive correlation structure but is nonlinear because its coefficients are random. The exponential distributional assumptions involved in this model highlight a very broad four parameter structure which combines five exponential random variables into a sixth exponential random variable; other applications of this structure are briefly considered. Dependency in the NEAR(2) process not accounted for by standard autocorrelations is explored by developing a residual analysis for time series having autoregressive correlation structure; this involves defining linear uncorrelated residuals which are dependent, and then assessing this higher order dependence by standard time series computations. Application of this residual analysis to the wind velocity data illustrates both the utility and difficulty of nonlinear time series modelling
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
NPS Report NumberNPS55-84-019
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Lawrance, A.J.; Lewis, P.A.W. (Wiley, 1985);An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by an analysis of a long series of wind velocity data which has first ...
Lewis, Peter A. W.; Lawrence, A. J. (Monterey, California. Naval Postgraduate School, 1983-04); NPS-55-83-008A second order autoregressive process in exponential variables, NEAR(2), is established: the distributional assumptions involved in this model highlight a yery broad four parameter structure which combines five ...
Higher order residual analysis for nonlinear time series with autoregressive correlation structures Lewis, Peter A.; Lawrance, Anthony J. (Monterey, California. Naval Postgraduate School, 1985-12); NPS55-85-030The paper considers nonlinear time series whose second order autocorrelations satisfy autoregressive Yule-Walker equations. The usual linear residuals are then uncorrelated, but not independent, as would be the case for ...