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

Helmut Pruscha

Stochastic Processes and their Applications, 1988, vol. 28, issue 2, 241-257

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.

Keywords: multivariate; point; processes; intensity; process; trend; component; detrending; asymptotic; parametric; inference; maximum; likelihood; approach (search for similar items in EconPapers)
Date: 1988
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