Lewis, Peter A. W.
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It is shown that the autoregressive, Markovian minification processes introduced by Tavares and Sim can be extended to marginal distributions other than the exponential and Weibull distributions. Necessary ans sufficient conditions on the hazard rate of the marginal distributions are given for a minification process to exist. Results are given for the derivation of the autocorrelation function; these correct the expression for the Weibull given by Sim. Monotonic transformations of the minification processes are also discussed and generate a whole new class of autoregressive processes with fixed marginal distributions. Processes generated by a maximum operation are also introduced and a comparison of three different Markovian processes with uniform marginal distributions are given. Keywords: Time series, Distribution functions, Biovariate distributions. (KR)
NPS Report NumberNPS55-88-010
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Lewis, Peter A. W. (Monterey, California. Naval Postgraduate School, 1978-11); NPS55-78-033Three models for positive-valued and discrete-valued stationary time series are discussed. All have the property that for a range of specified marginal distributions the time series have the same correlation structure as ...
Lewis, Peter A.W.; DeWald, Lee S. Sr.; McKenzie, Ed (1987);In many practical cases in time series analysis, marginal distributions in stationary situations are not Gaussian. It is therefore necessary to be able to generate and analyze nonGaussian time series. Several non-Gaussian ...
Dewald, Lee Samuel; McKenzie, Edward; Lewis, Peter A. W. (Monterey, California. Naval Postgraduate School, 1988-11); NPS-55-88-011A broad family of symmetric, thick tailed distributions, the £-Laplace distributions, is described. They are natural generalizations of the Laplace distribution. A family of random coefficient ARMA processes with £-Laplace ...