Skip to main content
SpringerLink
Log in

A Minimum Distance Lack-of-Fit Test in a Markovian Multiplicative Error Model

  • Original Article
  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

This paper proposes a lack-of-fit test for a parametric specification of the conditional mean function in a Markovian multiplicative error time series model. The proposed test is based on a minimized distance obtained using an integral of the square of a certain marked residual process. The asymptotic null distribution of the proposed test is model dependent and is not free from the underlying nuisance parameters. We propose a bootstrap method to implement the test and establish that the proposed bootstrap method is asymptotically valid. A finite sample simulation study that evaluates the empirical level and power is included. It compares the finite sample performance of the proposed test with several competing tests from the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balakrishna N, Koul HL, Sakhanenko L, Ossiander M (2019) Fitting a \(p\)th order parametric generalized linear autoregressive multiplicative error model. Sankhya Indian J Stat 81–B(Supplement 1):S103–S122

    MATH  Google Scholar 

  2. Bickel PJ, Freedman DA (1981) Some asymptotic theory for the bootstrap. Ann Stat 9:1196–21217

    MathSciNet  MATH  Google Scholar 

  3. Cavaliere G, Perera I, Rahbek A (2021) Specification tests for GARCH processes. Working paper

  4. Chen Y-T, Hsieh C-S (2010) Generalized moment tests for autoregressive conditional duration models. J Financ Econom 8:345–391

    Article  Google Scholar 

  5. Chou RY (2005) Forecasting financial volatilities with extreme values: the conditional autoregressive range (CARR) model. J Money Credit Bank 37(3):561–582

    Article  Google Scholar 

  6. Engle R (2002) New frontiers for ARCH models. J Appl Econom 17:425–446

    Article  Google Scholar 

  7. Engle RF, Gallo GM (2006) A multiple indicators model for volatility using intra-daily data. J Econom 131:3–27

    Article  MathSciNet  Google Scholar 

  8. Engle RF, Russell JR (1998) Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econom J Econom Soc 66:1127–1162

    MathSciNet  MATH  Google Scholar 

  9. Freedman DA (1981) Bootstrapping regression models. Ann Stat 9:1218–1228

    Article  MathSciNet  Google Scholar 

  10. Giacomini R, Politis DN, White H (2013) A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Econom Theory 29:567–589

    Article  MathSciNet  Google Scholar 

  11. Grammig J, Maurer K-O (2000) Non-monotonic hazard functions and the autoregressive conditional duration model. Econom J 3(1):16–38

    Article  Google Scholar 

  12. Guo B, Li S (2018) Diagnostic checking of Markov multiplicative error models. Econ Lett 170:139–142

    Article  MathSciNet  Google Scholar 

  13. Hall P, Heyde CC (1980) Martingale limit theory and its applications. Academic Press, New York

    MATH  Google Scholar 

  14. Hautsch N (2012) Econometrics of financial high-frequency data. Springer, Heidelberg

    Book  Google Scholar 

  15. Koul Hira L (2002) Weighted empirical processes in dynamic nonlinear models. Lecture notes series in statistics, vol 166, 2nd edn. Springer, New York

    Book  Google Scholar 

  16. Koul Hira L (2019) A uniform convergence result for weighted residual empirical processes. RM#719, Department of Statistics and Probability, MSU

  17. Koul HL, Stute W (1999) Nonparametric model checks for time series. Ann Stat 27:204–236

    Article  MathSciNet  Google Scholar 

  18. Koul HL, Perera I, Balakrishna N (2021) A class of minimum distance estimators in Markovian multiplicative error models. Working paper

  19. Koul HL, Perera I, Silvaphulle MJ (2012) Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models. Econom Theory 28:1283–1312

    Article  MathSciNet  Google Scholar 

  20. Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65:297–303

    Article  Google Scholar 

  21. Lunde A (1999) A generalized gamma autoregressive conditional duration model. Aalborg University, Discussion paper

  22. Manganelli S (2005) Duration, volume and volatility impact of trades. J Financ Mark 8(4):377–399

    Article  Google Scholar 

  23. Meitz M, Teräsvirta T (2006) Evaluating models of autoregressive conditional duration. J Bus Econ Stat 24:104–124

    Article  MathSciNet  Google Scholar 

  24. Pacurar M (2008) Autoregressive conditional duration models in finance: a survey of the theoretical and empirical literature. J Econ Surv 22:711–751

    Article  Google Scholar 

  25. Perera I, Koul HL (2017) Fitting a two phase threshold multiplicative error model. J Econom 197:348–367

    Article  MathSciNet  Google Scholar 

  26. Perera I, Silvapulle MJ (2020) Bootstrap based probability forecasting in multiplicative error models. J Econom 221:1–24

    Article  MathSciNet  Google Scholar 

  27. Stute W (1997) Nonparametric model checks for regression. Ann Stat 25(2):613–641

    Article  MathSciNet  Google Scholar 

  28. Stute W, Thies S, Zhu LX (1998) Model checks for regression: an innovation process approach. Ann Stat 26:1916–1934

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824-1027, USA

    Hira L. Koul

  2. Department of Economics, The University of Sheffield, Sheffield, S1 4DT, UK

    Indeewara Perera

Authors
  1. Hira L. Koul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Indeewara Perera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hira L. Koul.

Ethics declarations

No Conflict

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the topical collection “Celebrating the Centenary of Professor C. R. Rao” guest edited by , Ravi Khattree, Sreenivasa Rao Jammalamadaka, and M. B. Rao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koul, H.L., Perera, I. A Minimum Distance Lack-of-Fit Test in a Markovian Multiplicative Error Model. J Stat Theory Pract 15, 34 (2021). https://doi.org/10.1007/s42519-021-00168-1

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42519-021-00168-1

Keywords

Mathematics Subject Classification

Search

Navigation