AISM 54, 543-564

© 2002 ISM

## Power divergence family of tests for categorical time series models

### Konstantinos Fokianos

Department of Mathematics & Statistics, University of
Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus, e-mail: fokianos@ucy.ac.cy

(Received April 3, 2000; revised October 17, 2000)

Abstract.
A fundamental issue that arises after fitting a regression model
is that of testing the goodness of the fit. Our work brings together the power divergence family of goodness of fit tests and regression models for categorical time series.
We show that under some reasonable assumptions, the asymptotic
distribution of the power divergence family of goodness of fit
tests converges to a normal random variable. This fact introduces
a novel method for carrying out goodness of fit tests about
a regression model for categorical time series.
We couple the theory with some empirical results.

Key words and phrases:
Stochastic time dependent covariates, partial likelihood, martingale, logistic regression, multinomial logits, proportional odds, power.

**Source**
(TeX , DVI )