Simple models for positive-valued and discrete-valued time series with ARMA correlation structure
Lewis, Peter A. W.
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Three 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 the usual linear, autoregressive-moving average (ARMA) model. The models differ in the range of marginal distributions which can be accommodated and in the simplicity and flexibility of each model. Specifically the EARMA-type processes can be extended from the exponential distribution to a rather narrow range of continuous distributions; the DARMA-type processes can be defined usefully for any discrete marginal distribution and are simple and flexible. Finally the marginally controlled semiMarkov generated process can be defined for any continuous or discrete positive-valued distribution and is therefore very flexible. However, the model suffers from some complexity and parametric obscurity
NPS Report NumberNPS55-78-033
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Lewis, P.A.W.; Jacobs, P.A.; McKenzie, E. (1983);Time series models for positive-valued and discrete-valued input processes are discussed, with the emphasis on the simulation problems which arise in generating time series from these models.
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