Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 536--547

Approximating Dependence Structures of Repeated Stochastic Processes

By

Bertrand Clarke, University of British Columbia,Vancouver, Canada
Peter X.-K. Song, York University,Toronto, Canada

SUMMARY. We present a general procedure for joint modelling of the mean structure and the stochastic dependence for longitudinal data.  To reveal the underlying dependence mechanism, we proceed in three steps.  First, we use cross-sectional regression to relocate the data to achieve marginal stationarity. Second, we discretize the relocated data.   Third, we model the dependence structure of the discretized data as a stationary Markov chain with sufficiently high order. The procedure is primarily developed for continuous responses, but it is applicable for discrete responses that emerge from an underlying continuous process.  Two data analysis examples are presented to illustrate our procedure.

AMS (1991) subject classification}. Primary 62M10; secondary 62-10.

Key words and phrases. Discretization, longitudinal data, Markovity, nonstationarity.

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