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 -