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TESTING FOR EMBEDDABILITY BY STATIONARY REVERSIBLE CONTINUOUS-TIME MARKOV PROCESSES

Published online by Cambridge University Press:  01 December 1998

Jean-Pierre Florens
Affiliation:
Université des Sciences Sociales de Toulouse
Eric Renault
Affiliation:
CREST-INSEE
Nizar Touzi
Affiliation:
Université Paris IX Dauphine

Abstract

Given an observation of a discrete-time process {Yi,i = 0...n} assumed to be Markov, stationary, and time reversible, we develop a (conservative) test procedure of embeddability by a continuous-time reversible Markov process. The test statistic is derived from a set of moment inequality restrictions implied by the spectral properties of such continuous-time processes. Most interesting is that the embeddability condition of interest is a direct extension of the well-known embeddability problem by a two-state Markov chain. Empirical experiments show that the embeddability hypothesis is rejected more frequently for exchange rate daily data than for stock indices data.

Type
Research Article
Copyright
© 1998 Cambridge University Press

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