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Lack-Of-Fit Testing Of The Conditional Mean Function In A Class Of Markov Multiplicative Error Models


  • Koul, Hira L.
  • Perera, Indeewara
  • Silvapulle, Mervyn J.


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.

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  • Koul, Hira L. & Perera, Indeewara & Silvapulle, Mervyn J., 2012. "Lack-Of-Fit Testing Of The Conditional Mean Function In A Class Of Markov Multiplicative Error Models," Econometric Theory, Cambridge University Press, vol. 28(06), pages 1283-1312, December.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:06:p:1283-1312_00

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    Cited by:

    1. Ng, F.C. & Li, W.K. & Yu, Philip L.H., 2016. "Diagnostic checking of the vector multiplicative error model," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 86-97.
    2. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.

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