Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T12:19:18.104Z Has data issue: false hasContentIssue false
  • English
  • Français

LACK-OF-FIT TESTING OF THE CONDITIONAL MEAN FUNCTION IN A CLASS OF MARKOV MULTIPLICATIVE ERROR MODELS

Published online by Cambridge University Press:  21 May 2012

Hira L. Koul,
Indeewara Perera and
Mervyn J. Silvapulle
Hira L. Koul
Affiliation:
Michigan State University
Indeewara Perera*
Affiliation:
Monash University
Mervyn J. Silvapulle
Affiliation:
Monash University
*
*Address correspondence to Indeewara Perera, Department of Econometrics and Business Statistics, Monash University, P.O. Box 197, Caulfield East, Australia 3145; e-mail: indeewara.perera@monash.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 6 , December 2012, pp. 1283 - 1312
Copyright
Copyright © Cambridge University Press 2012 

References

REFERENCES

Bauwens, L. (2006) Econometric analysis of intra-daily trading activity on the Tokyo stock exchange. Monetary and Economic Studies 24, 1–23.Google Scholar
Bauwens, L. & Veredas, D. (2004) The stochastic conditional duration model: A latent factor model for the analysis of financial durations. Journal of Econometrics 119, 381–412.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
Box, G.E.P. & Jenkins, G.M. (1976) Time Series Analysis: Forecasting and Control, rev. ed. Holden-Day.Google Scholar
Brownlees, C.T., Cipollini, F., & Gallo, G.M. (2011) Multiplicative Error Models. Econometrics working papers archive, Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti."Google Scholar
Chang, M.N. (1990) Weak convergence of a self-consistent estimator of the survival function with doubly censored data. Annals of Statistics 18, 391–404.CrossRefGoogle Scholar
Chen, Y.-T. & Hsieh, C.-S. (2010) Generalized moment tests for autoregressive conditional duration models. Journal of Financial Econometrics 8, 345–391.CrossRefGoogle Scholar
Chou, R.Y. (2005) Forecasting financial volatilities with extreme values: The conditional autoregressive range (CARR) model. Journal of Money, Credit and Banking 37, 561–582.Google Scholar
Chow, Y.S. & Teicher, H. (1978) Probability Theory. Springer-Verlag.CrossRefGoogle Scholar
Datta, S. & McCormick, W.P. (1995) Bootstrap inference for a first-order autoregression with positive innovations. Journal of the American Statistical Association 90, 1289–1300.CrossRefGoogle Scholar
Dette, H. & Hetzler, B. (2009) Khmaladze transformation of integrated variance processes with applications to goodness-of-fit testing. Mathematical Methods of Statistics 18, 97–116.CrossRefGoogle Scholar
Engle, R. (2002) New frontiers for ARCH models. Journal of Applied Econometrics 17, 425–446.CrossRefGoogle Scholar
Engle, R.F. & Gallo, G.M. (2006) A multiple indicators model for volatility using intra-daily data. Journal of Econometrics 131, 3–27.CrossRefGoogle Scholar
Engle, R.F., Gallo, G.M., & Velucchi, M. (2012) Volatility spillovers in East Asian financial markets: A MEM-based approach. Review of Economics and Statistics 94, 222–233.CrossRefGoogle Scholar
Engle, R.F. & Russell, J.R. (1998) Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica 66, 1127–1162.CrossRefGoogle Scholar
Escanciano, J.C. (2010) Asymptotic distribution-free diagnostic tests for heteroskedastic time series models. Econometric Theory 26, 744–773.CrossRefGoogle Scholar
Escanciano, J.C. & Mayoral, S. (2010) Data-driven smooth tests for the martingale difference hypothesis. Computational Statistics & Data Analysis 54, 1983–1998.CrossRefGoogle Scholar
Fernandes, M. & Grammig, J. (2005) Nonparametric specification tests for conditional duration models. Journal of Econometrics 127, 35–68.CrossRefGoogle Scholar
Ghysels, E., Gouriéroux, C., & Jasiak, J. (2004) Stochastic volatility duration models. Journal of Econometrics 119, 413–433.CrossRefGoogle Scholar
Giot, P. (2000) Time transformations, intraday data, and volatility models. Journal of Computational Finance 4, 31–62.CrossRefGoogle Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application. Academic Press.Google Scholar
Hautsch, N. (2006) Testing the Conditional Mean Function of Autoregressive Conditional Duration Models. FRU Working papers 2006/06, University of Copenhagen, Department of Economics, Finance Research Unit.CrossRefGoogle Scholar
Hong, Y. & Lee, T.-H. (2003) Diagnostic checking for the adequacy of nonlinear time series models. Econometric Theory 19, 1065–1121.CrossRefGoogle Scholar
Hong, Y. & Lee, Y.-J. (2011) Detecting misspecifications in autoregressive conditional duration models and non-negative time-series processes. Journal of Time Series Analysis 32, 1–32.CrossRefGoogle Scholar
Jasiak, J. (1998) Persistence in intertrade durations. Finance 19, 166–195.Google Scholar
Khmaladze, È.V. (1981) A martingale approach in the theory of goodness-of-fit tests. Akademiya Nauk SSSR. Teoriya Veroyatnosteǐ ee Primeneniya 26, 246–265.Google Scholar
Khmaladze, E.V. & Koul, H.L. (2004) Martingale transforms goodness-of-fit tests in regression models. Annals of Statistics 32, 995–1034.CrossRefGoogle Scholar
Koul, H.L. & Song, W. (2010) Conditional variance model checking. Journal of Statistical Planning and Inference 140, 1056–1072.CrossRefGoogle Scholar
Koul, H.L. & Stute, W. (1999) Nonparametric model checks for time series. Annals of Statistics 27, 204–236.Google Scholar
Lanne, M. (2006) A mixture multiplicative error model for realized volatility. Journal of Financial Econometrics 4, 594–616.CrossRefGoogle Scholar
Ling, S. & Tong, H. (2011) Score based goodness-of-fit tests for time series. Statistica Sinica 21, 1807–1829.CrossRefGoogle Scholar
Ljung, G.M. & Box, G.E.P. (1978) On a measure of lack of fit in time series models. Biometrika 65, 297–303.CrossRefGoogle Scholar
Luca, G.D. & Gallo, G. (2004) Mixture processes for financial intradaily durations. Studies in Nonlinear Dynamics & Econometrics 8, 1–12.Google Scholar
Manganelli, S. (2005) Duration, volume and volatility impact of trades. Journal of Financial Markets 8, 377–399.CrossRefGoogle Scholar
Meitz, M. & Teräsvirta, T. (2006) Evaluating models of autoregressive conditional duration. Journal of Business & Economic Statistics 24, 104–124.CrossRefGoogle Scholar
Pacurar, M. (2008) Autoregressive conditional duration models in finance: A survey of the theoretical and empirical literature. Journal of Economic Surveys 22, 711–751.CrossRefGoogle Scholar
Stone, C. (1963) Weak convergence of stochastic processes defined on semi-infinite time intervals. Proceedings of the American Mathematical Society 14, 694–696.CrossRefGoogle Scholar
Stute, W., Thies, S., & Zhu, L.X. (1998) Model checks for regression: An innovation process approach. Annals of Statistics 26, 1916–1934.Google Scholar
Stute, W., Xu, W.L., & Zhu, L.X. (2008) Model diagnosis for parametric regression in high-dimensional spaces. Biometrika 95, 451–467.CrossRefGoogle Scholar
Tsay, R.S. (2010) Analysis of Financial Time Series, 3rd ed. Wiley Series in Probability and Statistics. Wiley.CrossRefGoogle Scholar
von Neumann, J. (1941) Distribution of the ratio of the mean square successive difference to the variance. Annals of Mathematical Statistics 12, 367–395.CrossRefGoogle Scholar
Wooldridge, J.M. (1990) A unified approach to robust, regression-based specification tests. Econometric Theory 6, 17–43.CrossRefGoogle Scholar