Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-07-07T23:16:26.909Z Has data issue: false hasContentIssue false
  • English
  • Français

SPECIFICATION TESTS FOR MULTIPLICATIVE ERROR MODELS

Published online by Cambridge University Press:  23 February 2016

Indeewara Perera  and
Mervyn J. Silvapulle
Indeewara Perera*
Affiliation:
Monash University
Mervyn J. Silvapulle*
Affiliation:
Monash University
*
*Please address correspondence to: Indeewara Perera/Mervyn Silvapulle, Department of Econometrics and Business Statistics, Monash Business School, Monash University, P.O. Box 197, Caulfield East, Australia 3145; e-mail: indeewara.perera@monash.edu; mervyn.silvapulle@monash.edu.
*Please address correspondence to: Indeewara Perera/Mervyn Silvapulle, Department of Econometrics and Business Statistics, Monash Business School, Monash University, P.O. Box 197, Caulfield East, Australia 3145; e-mail: indeewara.perera@monash.edu; mervyn.silvapulle@monash.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

The family of multiplicative error models is important for studying non-negative variables such as realized volatility, trading volume, and duration between consecutive financial transactions. Methods are developed for testing the parametric specification of a multiplicative error model, which consists of separate parametric models for the conditional mean and the error distribution. The same method can also be used for testing the specification of the error distribution provided the conditional mean is correctly specified. A bootstrap method is proposed for computing the p-values of the tests and is shown to be consistent. The proposed tests have nontrivial asymptotic power against a class of O(n−1/2)-local alternatives. The tests performed well in a simulation study, and they are illustrated using a data example on realized volatility.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 2 , April 2017 , pp. 413 - 438
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bauwens, L. & Giot, P. (2001) Econometric Modeling of Stock Market Intraday Activity . Advanced Studies in Theoretical and Applied Econometrics, vol. 38. Kluwer Academic Publishers.Google Scholar
Bauwens, L., Grammig, J., Veredas, D., & Giot, P. (2004) A comparison of financial duration models via density forecasts. International Journal of Forecasting 20, 589–609.CrossRefGoogle Scholar
Brownlees, C.T. & Gallo, G.M. (2006) Financial econometric analysis at ultra-high frequency: Data handling concerns. Computational Statistics & Data Analysis 51, 2232–2245.CrossRefGoogle Scholar
Brownlees, C.T., Cipollini, F., & Gallo, G.M. (2012) Multiplicative error models. In Bauwens, L., Hafner, C., & Laurent, S. (eds.), Handbook of Volatility Models and Their Applications, Chapter 9, pp. 225–247. Wiley.Google 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.CrossRefGoogle Scholar
Corradi, V. & Swanson, N.R. (2006) Bootstrap conditional distribution tests in the presence of dynamic misspecification. Journal of Econometrics 133, 779–806.CrossRefGoogle Scholar
Corsi, F., Mittnik, S., Pigorsch, C., & Pigorsch, U. (2008) The volatility of realized volatility. Econometric Reviews 27, 46–78.CrossRefGoogle Scholar
Diebold, F.X., Gunther, T.A., & Tay, A.S. (1998) Evaluating density forecasts with applications to financial risk management. International Economic Review 39, 863–883.CrossRefGoogle Scholar
Engle, R.F. (2000) The Econometrics of ultra-high-frequency data. Econometrica 68, 1–22.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. & Russell, J.R. (1998) Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica 66, 1127–1162.CrossRefGoogle Scholar
Fernandes, M. & Grammig, J. (2005) Nonparametric specification tests for conditional duration models. Journal of Econometrics 127, 35–68.CrossRefGoogle Scholar
Fernandes, M. & Grammig, J. (2006) A family of autoregressive conditional duration models. Journal of Econometrics 130, 1–23.CrossRefGoogle Scholar
Freedman, D.A. (1975) On tail probabilities for martingales. Annals of Probability 3, 100–118.CrossRefGoogle Scholar
Ghysels, E., Gouriéroux, C., & Jasiak, J. (2004) Stochastic volatility duration models. Journal of Econometrics 119, 413–433.CrossRefGoogle Scholar
Giacomini, R., Politis, D.N., & White, H. (2013) A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Econometric Theory 29, 567–589.CrossRefGoogle Scholar
Giot, P. (2000) Time transformations, intraday data, and volatility models. Journal of Computational Finance 4, 31–62.CrossRefGoogle Scholar
Hautsch, N. (2011) Econometrics of Financial High-Frequency Data. Springer.Google Scholar
Janssen, P., Swanepoel, J., & Veraverbeke, N. (2005) Bootstrapping modified goodness-of-fit statistics with estimated parameters. Statistics & Probability Letters 71, 111–121.CrossRefGoogle Scholar
Koul, H.L. & Ling, S. (2006) Fitting an error distribution in some heteroscedastic time series models. The Annals of Statistics 34, 994–1012.CrossRefGoogle Scholar
Koul, H.L. & Ossiander, M. (1994) Weak convergence of randomly weighted dependent residual empiricals with applications to autoregression. The Annals of Statistics 22, 540–562.CrossRefGoogle Scholar
Koul, H.L., Perera, I., & Silvapulle, M.J. (2012) Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models. Econometric Theory 28, 1283–1312.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
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
Ossiander, M. (1987) A central limit theorem under metric entropy with L 2 bracketing. The Annals of Probability 15, 897–919.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
Straumann, D. & Mikosch, T. (2006) Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach. The Annals of Statistics 34, 2449–2495.CrossRefGoogle Scholar
Supplementary material: File

Perera and Silvapulle supplementary material S1

Perera and Silvapulle supplementary material

Download Perera and Silvapulle supplementary material S1(File)
File 51.3 KB
Supplementary material: PDF

Perera and Silvapulle supplementary material S2

Perera and Silvapulle supplementary material

Download Perera and Silvapulle supplementary material S2(PDF)
PDF 180.1 KB
Supplementary material: File

Perera and Silvapulle supplementary material S3

Perera and Silvapulle supplementary material

Download Perera and Silvapulle supplementary material S3(File)
File 32.8 KB
Supplementary material: File

Perera and Silvapulle supplementary material S4

Perera and Silvapulle supplementary material

Download Perera and Silvapulle supplementary material S4(File)
File 91.9 KB