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

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

Abstract

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.

Suggested Citation

  • 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(6), pages 1283-1312, December.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:06:p:1283-1312_00
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    Citations

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    Cited by:

    1. Perera, Indeewara & Silvapulle, Mervyn J., 2021. "Bootstrap based probability forecasting in multiplicative error models," Journal of Econometrics, Elsevier, vol. 221(1), pages 1-24.
    2. 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.
    3. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.
    4. N. Balakrishna & H. L. Koul & M. Ossiander & L. Sakhanenko, 2019. "Fitting a pth Order Parametric Generalized Linear Autoregressive Multiplicative Error Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 103-122, September.
    5. Giuseppe Cavaliere & Indeewara Perera & Anders Rahbek, 2021. "Specification tests for GARCH processes," Discussion Papers 21-06, University of Copenhagen. Department of Economics.
    6. Hira L. Koul & Indeewara Perera & Narayana Balakrishna, 2023. "A class of Minimum Distance Estimators in Markovian Multiplicative Error Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 87-115, May.
    7. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.
    8. Guo, Bin & Li, Shuo, 2018. "Diagnostic checking of Markov multiplicative error models," Economics Letters, Elsevier, vol. 170(C), pages 139-142.
    9. Fabrizio Cipollini & Giampiero M. Gallo, 2021. "Multiplicative Error Models: 20 years on," Papers 2107.05923, arXiv.org.
    10. Ke, Rui & Lu, Wanbo & Jia, Jing, 2021. "Evaluating multiplicative error models: A residual-based approach," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

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