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Published online by Cambridge University Press:  21 May 2012

Hira L. Koul
Michigan State University
Indeewara Perera*
Monash University
Mervyn J. Silvapulle
Monash University
*Address correspondence to Indeewara Perera, Department of Econometrics and Business Statistics, Monash University, P.O. Box 197, Caulfield East, Australia 3145; e-mail:


The family of multiplicative error models, introduced by Engle (2002, Journal of Applied Econometrics 17, 425–446), has attracted considerable attention in recent literature for modeling positive random variables, such as the duration between trades at a stock exchange, volume transactions, and squared log returns. Such models are also applicable to other positive variables such as waiting time in a queue, daily/hourly rainfall, and demand for electricity. This paper develops a new method for testing the lack-of-fit of a given parametric multiplicative error model having a Markov structure. The test statistic is of Kolmogorov–Smirnov type based on a particular martingale transformation of a marked empirical process. The test is asymptotically distribution free, is consistent against a large class of fixed alternatives, and has nontrivial asymptotic power against a class of nonparametric local alternatives converging to the null hypothesis at the rate of O (n–1/2). In a simulation study, the test performed better overall than the general purpose Ljung–Box Q-test, a Lagrange multiplier type test, and a generalized moment test. We illustrate the testing procedure by considering two data examples.

Copyright © Cambridge University Press 2012 

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