Advertisement

Sankhya B

pp 1–20 | Cite as

Fitting a pth Order Parametric Generalized Linear Autoregressive Multiplicative Error Model

  • N. BalakrishnaEmail author
  • H. L. Koul
  • M. Ossiander
  • L. Sakhanenko
Article
  • 1 Downloads

Abstract

This paper is concerned with the problem of fitting a generalized linear model to the conditional mean function of multiplicative error time series models. These models are particularly suited to model nonnegative time series such as the duration between trades at a stock exchange and volume transactions. The proposed test, based on a marked residual empirical process whose marks are suitably defined residuals and which jumps at the estimated indices, is shown to be asymptotically distribution free.

Keywords and phrases

Martingale transform AR conditional duration models 

AMS (2000) subject classification

Primary 62M02 Secondary 62M10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

Authors would like to thank the referees for their thoughtful comments that helped to improve the presentation.

References

  1. Engle, R. F. and Russell, J. R. (1998). Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica 66, 5, 1127–1162.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Engle, R. F. (2002). New frontiers for ARCH models. J. Applied Econometrics 17, 425–446.CrossRefGoogle Scholar
  3. Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Applications. Academic Press, New York.zbMATHGoogle Scholar
  4. Hautsch, N. (2012). Econometrics of Financial High-Frequency Data. Springer, Heidelberg.CrossRefzbMATHGoogle Scholar
  5. Khmaladze, E. V. and Koul, H. L. (2004). Martingale transforms goodness-of-fit tests in regression models. Ann. Statist. 32, 995–1034.MathSciNetCrossRefzbMATHGoogle Scholar
  6. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13–30.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Khmaladze, E. V. and Koul, H. L. (2009). Goodness-of-fit problem for errors in nonparametric regression: distribution free approach. Ann. Statist. 37, 3165–3185.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Koul, H. L. and Stute, W. (1999). Nonparametric model checks for time series. Ann. Statist. 27, 204–236.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Koul, H. L., Perera, I. and Silvapulle, M. J. (2012). Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models. Econometric Theory 28, 6, 1283–1312.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Meitz, M. and Teräsvirta, T. (2006). Evaluating models of autoregressive conditional duration. J. Business & Economic Statist. 24, 104–124.MathSciNetCrossRefGoogle Scholar
  11. Mnatsakanov, R. and Sarkisian, K. (2012). Varying kernel density estimation on \(\mathbb {\mathbb {R}}_{+}\). Statistics & Probability Letters 82, 1337–1345.MathSciNetCrossRefzbMATHGoogle Scholar
  12. Pacurar, M. (2008). Autoregressive conditional duration models in finance: a survey of the theoretical and empirical literature. J. Economic Surveys 22, 711–751.CrossRefGoogle Scholar
  13. Resnick, S. (1992). Adventures in Stochastic Processes. Birkhuser, Boston.zbMATHGoogle Scholar
  14. Stute, W., Thies, S. and Zhu, L. (1998). Model checks for regression: an innovation process approach. Annal. Statist. 26, 5, 19161934.MathSciNetzbMATHGoogle Scholar
  15. Stute, W. and Zhu, Li-xing (2002). Model checks for generalized linear models, Scand. J. Statist. 29, 535–545.MathSciNetzbMATHGoogle Scholar
  16. van der Vaart, A. W. and Wellner, J. (1996). Weak Convergence and Empirical Processes with Applications to Statistics. Springer-Verlag, New York.CrossRefzbMATHGoogle Scholar

Copyright information

© Indian Statistical Institute 2019

Authors and Affiliations

  • N. Balakrishna
    • 1
    Email author
  • H. L. Koul
    • 2
  • M. Ossiander
    • 3
  • L. Sakhanenko
    • 2
  1. 1.Cochin University of Science and TechnologyKochiIndia
  2. 2.Michigan State UniversityEast LansingUSA
  3. 3.Oregon State UniversityCorvallisUSA

Personalised recommendations