Skip to main content
SpringerLink
Log in

An omnibus test to detect time-heterogeneity in time series

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

This paper focuses on a procedure to test for structural changes in the first two moments of a time series, when no information about the process driving the breaks is available. We model the series as a finite-order auto-regressive process plus an orthogonal Bernstein polynomial to capture heterogeneity. Testing for the null of time-invariance is then achieved by testing the order of the polynomial, using either an information criterion, or a restriction test. The procedure is an omnibus test in the sense that it covers both the pure discrete structural changes and some continuous changes models. To some extent, our paper can be seen as an extension of Heracleous et al. (Econom Rev 27:363–384, 2008).

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Akaike H (1974) Stochastic theory of minimal realization. IEEE Trans Automat Contr 667–674

  • Altissimo F, Corradi V (2003) Strong rules for detecting the number of breaks in a time series. J Econom 117:207–244

    Article  MathSciNet  MATH  Google Scholar 

  • Andrews WK (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61:821–856

    Article  MathSciNet  MATH  Google Scholar 

  • Andrews WK, Ploberger W (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62:1383–1414

    Article  MathSciNet  MATH  Google Scholar 

  • Bai J (1999) Likelihood ratio tests for multiple structural changes. J Econom 91:299–323

    Article  MATH  Google Scholar 

  • Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78

    Article  MathSciNet  MATH  Google Scholar 

  • Bai J, Perron P (2003) Computation and analysis of multiple structural change models. J Appl Econom 18:1–22

    Article  Google Scholar 

  • Baek C, Pipiras V (2011) Statistical tests for changes in mean against long-range dependence. J Time Ser Anal 33:131–151

    Article  MathSciNet  Google Scholar 

  • Berkes I, Horvath L, Kokozka P, Shao Q-M (2006) On discriminating between long-range dependence and changes in mean. Ann Stat 34:1140–1165

    Article  MATH  Google Scholar 

  • Brown RL, Durbin J, Evans M (1975) Techniques for testing the constancy of regression relationships over time. J R Stat Soc 37:149–192

    MathSciNet  MATH  Google Scholar 

  • Charfeddine L, Guégan D (2011) Which is the best model for the US inflation rate : a structural changes model or a long memory process? IUP J Appl Econ 1:5–25

    Google Scholar 

  • Davidson R, MacKinnon JG (2004) Econometric theory and methods. Oxford University Press, Oxford

    Google Scholar 

  • Engle RF, Smith AD (1999) Stochastic permanent breaks. Rev Econ Stat 81:553–574

    Article  Google Scholar 

  • Guégan D (2010) Non-stationary samples and meta-distribution. In: Basu A, Samanta T, SenGupta A (eds), ISI Platinium Jubilee Volume, Statistical sciences and interdisciplinary research, ICSPRAR World Scientific Review

  • Hansen BE (2000) Testing for structural changes in conditional models. J Econom 97:93–115

    Article  MATH  Google Scholar 

  • Heracleous MS, Koutris A, Spanos A (2008) Testing for nonstationarity using maximum entropy resampling: a misspecification testing perspective. Econom Rev 27:363–384

    Article  MathSciNet  MATH  Google Scholar 

  • Granger C, Starica C (2005) Nonstationarities in stock returns. Rev Econ Stat 87:503–522

    Article  Google Scholar 

  • MacNeill IB (1978) Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times. Ann Stat 6:422–433

    Article  MathSciNet  MATH  Google Scholar 

  • McQuarrie ADR, Tsai C-L (1998) Regression and time series model selection. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Nyblom J (1989) Testing for the constancy of parameters over time. J Am Stat Assoc 84:223–230

    Article  MathSciNet  MATH  Google Scholar 

  • Perron P (1989) The great crash, the oil price shock and the unit root hypothesis. Econometrica 57: 1361–1401

    Article  MATH  Google Scholar 

  • Perron P (1991) A test for changes in a polynomial trend function for a dynamic time series. Research Memorandum No. 363. Econometric Research Program. Princeton University, Princeton

    Google Scholar 

  • Perron P (2005) Dealing with structural breaks. In: Palgrave handbook of econometrics vol 1: econometric theory

Download references

Author information

Authors and Affiliations

  1. Centre d’Economie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne, 106-112 Boulevard de l’Hopital, 75013 , Paris, France

    Dominique Guégan & Philippe de Peretti

Authors
  1. Dominique Guégan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe de Peretti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe de Peretti.

Appendix: Results of Monte-Carlo simulations

Appendix: Results of Monte-Carlo simulations

See Tables 1, 2, 3, 4, 5, 6 and 7

 

Table 1 \(AICu\) based criterion for five models, the last four ones exhibiting ruptures in mean
Full size table
Table 2 Empirical size and power of restriction tests at 4 nominal sizes for five models, the last four ones exhibiting ruptures in mean
Full size table
Table 3 Empirical size and power of the Andrews–Ploberger test at the 5 % nominal size, for five models, the last four ones exhibiting ruptures in mean
Full size table
Table 4 Empirical size and power of the CUSUM test at the 5 % nominal size, for five models, the last four ones exhibiting ruptures in mean
Full size table
Table 5 \(AICu\) based criterion for four models, the last three ones exhibiting ruptures in variance
Full size table
Table 6 Empirical size and power of restriction tests at 4 nominal sizes for four models, the last three ones exhibiting ruptures in variance
Full size table
Table 7 Empirical size and power of the CUSUM test at the 5 % nominal size for four models, the last three ones exhibiting ruptures in variance
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guégan, D., de Peretti, P. An omnibus test to detect time-heterogeneity in time series. Comput Stat 28, 1225–1239 (2013). https://doi.org/10.1007/s00180-012-0356-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-012-0356-7

Keywords

Search

Navigation