Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models

Hira Koul, Indeewara Perera, Mervyn Joseph Silvapulle

Research output: Contribution to journalArticleResearchpeer-review

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.
Original languageEnglish
Pages (from-to)1283 - 1312
Number of pages30
JournalEconometric Theory
Volume28
Issue number6
DOIs
Publication statusPublished - 2012

Cite this

@article{cd1fd7e047e64df293677a2cd11df1e0,
title = "Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models",
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.",
author = "Hira Koul and Indeewara Perera and Silvapulle, {Mervyn Joseph}",
year = "2012",
doi = "10.1017/S0266466612000102",
language = "English",
volume = "28",
pages = "1283 -- 1312",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "6",

}

Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models. / Koul, Hira; Perera, Indeewara; Silvapulle, Mervyn Joseph.

In: Econometric Theory, Vol. 28, No. 6, 2012, p. 1283 - 1312.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models

AU - Koul, Hira

AU - Perera, Indeewara

AU - Silvapulle, Mervyn Joseph

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1017/S0266466612000102

DO - 10.1017/S0266466612000102

M3 - Article

VL - 28

SP - 1283

EP - 1312

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 6

ER -