LACK-OF-FIT TESTING OF THE CONDITIONAL MEAN FUNCTION IN A CLASS OF MARKOV MULTIPLICATIVE ERROR MODELS
The family of multiplicative error models, introduced by Engle (<xref>2002</xref>, <italic>Journal of Applied Econometrics</italic> 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 <italic>O</italic> (<italic>n</italic> <sup>–1/2</sup>). In a simulation study, the test performed better overall than the general purpose Ljung–Box <italic>Q</italic>-test, a Lagrange multiplier type test, and a generalized moment test. We illustrate the testing procedure by considering two data examples.
Year of publication: |
2012
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Authors: | Koul, Hira L. ; Perera, Indeewara ; Silvapulle, Mervyn J. |
Published in: |
Econometric Theory. - Cambridge University Press. - Vol. 28.2012, 06, p. 1283-1312
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Publisher: |
Cambridge University Press |
Description of contents: | Abstract [journals.cambridge.org] |
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