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Computational Statistics

, Volume 27, Issue 4, pp 779–797 | Cite as

Hybrid bootstrap aided unit root testing

  • C. Jentsch
  • J.-P. Kreiss
  • P. MantalosEmail author
  • E. Paparoditis
Original Paper
  • 273 Downloads

Abstract

In this paper, we propose a hybrid bootstrap procedure for augmented Dickey-Fuller (ADF) tests for the presence of a unit root. This hybrid proposal combines a time domain parametric autoregressive fit to the data and a nonparametric correction applied in the frequency domain to capture features that are possibly not represented by the parametric model. It is known that considerable size and power problems can occur in small samples for unit root testing in the presence of an MA parameter using critical values of the asymptotic Dickey-Fuller distribution. The benefit of the sieve bootstrap in this situation has been investigated by Chang and Park (J Time Ser Anal 24:379–400, 2003). They showed asymptotic validity as well as substantial improvements for small sample sizes, but the actual sizes of their bootstrap tests were still quite far away from the nominal size. The finite sample performances of our procedure are extensively investigated through Monte Carlo simulations and compared to the sieve bootstrap approach. Regarding the size of the tests, our results show that the hybrid bootstrap remarkably outperforms the sieve bootstrap.

Keywords

Hybrid bootstrap Sieve bootstrap Unit root testing ADF tests 

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References

  1. Akaike, H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csáki F (eds) Proceedings of the 2nd International Symposium on Information Theory, Akademiai Kaido, Budapest, pp 267–281Google Scholar
  2. Beltrão KI, Bloomfield P (1987) Determining the bandwidth of a kernel spectrum estimate. J Time Ser Anal 8: 21–38MathSciNetzbMATHCrossRefGoogle Scholar
  3. Bühlmann P (1997) Sieve bootstrap for time series. Bernoulli 3: 48–123CrossRefGoogle Scholar
  4. Bühlmann P (1998) Sieve bootstrap for smoothing in nonstationary time series. Ann Stat 26: 48–83zbMATHCrossRefGoogle Scholar
  5. Chang Y, Park JY (2003) A sieve bootstrap for the test of a unit root. J Time Ser Anal 24: 379–400MathSciNetzbMATHCrossRefGoogle Scholar
  6. Dahlhaus R, Janas D (1996) A frequency domain bootstrap for ratio statistics in time series analysis. Ann Stat 24: 1934–1963MathSciNetzbMATHCrossRefGoogle Scholar
  7. Davidson R, MacKinnon JG (1998) Graphical methods for investigating the size and power of test statistics. Manch Sch 66: 1–26CrossRefGoogle Scholar
  8. Dickey DA, Fuller WA (1979) Distribution of estimators for autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431MathSciNetzbMATHGoogle Scholar
  9. Dickey DA, Fuller WA (1981) Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49: 1057–1072MathSciNetzbMATHCrossRefGoogle Scholar
  10. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 20(1): 121–145MathSciNetGoogle Scholar
  11. Franke J, Härdle W (1992) On Bootstrapping kernel spectral estimates. Ann Stat 2: 121–145CrossRefGoogle Scholar
  12. Fuller WA (1996) Introduction to statistical time series, 2nd (edn). Wiley, New YorkzbMATHGoogle Scholar
  13. Hall P, Horowitz JL (1996) Bootstrap critical values for tests based on generalized method of moments estimators with dependent data. Econometrica 64: 891–916MathSciNetzbMATHCrossRefGoogle Scholar
  14. Jentsch C, Kreiss J-P (2010) The multiple hybrid bootstrap—resampling multivariate linear processes. J Multivar Anal 101: 2320–2345MathSciNetzbMATHCrossRefGoogle Scholar
  15. Kreiss J-P (1998) Assymptotical Inference for a Class of Stochastic Processes. Habilitationsschrift, Universität HamburgmGoogle Scholar
  16. Kreiss J-P (1992) Bootstrap procedures for AR(∞) processes. In: Jöckel KH, Rothe G, Senders W (eds) Bootstrapping and related techniques, lecture notes in economics and mathematical systems 376, Heidelberg, SpringerGoogle Scholar
  17. Kreiss J-P, Paparoditis E (2003) Autoregressive-aided periodogram bootstrap for time series. Ann Stat 31(6): 1923–1955MathSciNetzbMATHCrossRefGoogle Scholar
  18. Künsch HR (1989) The jackknife and the bootstrap for general stationary observations. Ann Stat 17: 1217–1241zbMATHCrossRefGoogle Scholar
  19. Paparoditis E (2002) Frequency domain bootstrap for time series. In: Dehling H, Mikosch T, Sorensen M (eds) Empirical process techniques for dependent data. Birkhäuser, Boston, pp 365–381CrossRefGoogle Scholar
  20. Paparoditis E, Politis DN (1999) The local bootstrap for the periodogram. J Time Ser Anal 20: 193–222MathSciNetzbMATHCrossRefGoogle Scholar
  21. Paparoditis E, Politis DN (2001) Tapered block bootstrap. Biometrika 88: 19–1105MathSciNetCrossRefGoogle Scholar
  22. Paparoditis E, Politis DN (2001) The tapered block bootstrap for general statistics from stationary sequences. Econom J 5: 48–131MathSciNetGoogle Scholar
  23. Paparoditis E, Politis DN (2003) Residual-based block bootstrap for unit root testing. Econometrica 71: 813–855MathSciNetzbMATHCrossRefGoogle Scholar
  24. Psaradakis Z (2001) Bootstrap tests for an autoregressive unit root in the presence of weakly dependent errors. J Time Ser Anal 22: 577–594MathSciNetzbMATHCrossRefGoogle Scholar
  25. Said SE, Dickey DA (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71: 599–608MathSciNetzbMATHCrossRefGoogle Scholar
  26. Schwert GW (1989) Tests for unit roots: a Monte Carlo investigation. J Bus Econ Stat 7: 5–17MathSciNetGoogle Scholar
  27. Swensen AR (2003) Bootstrapping unit root tests for integrated processes. J Time Ser Anal 24: 99–126MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • C. Jentsch
    • 1
  • J.-P. Kreiss
    • 2
  • P. Mantalos
    • 3
    Email author
  • E. Paparoditis
    • 4
  1. 1.Department of EconomicsUniversity of MannheimMannheimGermany
  2. 2.Institut für Mathematische StochastikTechnische Universität BraunschweigBraunschweigGermany
  3. 3.Department of Statistics, Swedish Business SchoolUniversity of ÖrebroÖrebroSweden
  4. 4.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus

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