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Estimating a parametric trend component in a continuous-time jump-type process

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  • Pruscha, Helmut

Abstract

We consider stochastic processes with continuous time parameter and discrete state space processing an intensity process. We assume that the intensity process depends on a parameter [beta], the maximum likelihood (m.l.) estimator of which enjoys the usual asymptotic properties. Now a trend is defined by a factor multiplied to the intensity which may depend on a parameter [alpha]. We present two different types of trend functions (polynominal and reciprocal functions) under which the asymptotic properties of are inherited by the m.l. estimator () of ([alpha],[beta]). These trend functions, in particular, can be consistently estimated. Examples where the theory presented applies are Markov processes of jump-type, Markov branching processes with immigration and linear OM- (or learning-) processes.

Suggested Citation

  • Pruscha, Helmut, 1988. "Estimating a parametric trend component in a continuous-time jump-type process," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 241-257, June.
    • Handle: RePEc:eee:spapps:v:28:y:1988:i:2:p:241-257
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