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Bootstrap Unit Root Tests for Heavy-Tailed Time Series

  • Piotr Kokoszka
  • Andrejus Parfionovas

Abstract

We explore the applicability of bootstrap unit root tests to time series with heavy-tailed errors. The size and power of the tests are investigated using simulated data. Applications to financial time series are also presented. Two different bootstrap methods and the subsampling approach are compared. Conclusions on the optimal bootstrap parameters, the range of applicability, and the performance of the tests are presented.

Keywords

Unit Root Unit Root Test Null Distribution Yield Curve Bootstrap Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Arcones, M. and Giné, E. (1989) The bootstrap of the mean with arbitrary bootstrap sample size. Annals of the Institute Henri Poincaré, 22, 457–481.Google Scholar
  2. [2]
    Athreya, K. B. (1987) Bootstrap of the mean in the infinite variance case. The Annals of Statistics, 15:2,724–731.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Basawa, I. V., Mallik, A. K., McCormick, W. P., and Taylor, R. L. (1991) Bootstrap test of significance and sequential bootstrap estimation for unstable first order autoregressive processes. Communications in Statististics Theory and Methods, 20, 1015–1026.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Chan, N. H. and Tran, L. T. (1989) On the first order autoregressive process with infinite variance. Econometric Theory, 5, 354–362.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Davis, R. A. and Resnick, S. I. (1985) Limit theory for moving averages of random variables with regularly varying tail probabilities. The Annals of Probability, 13:1, 179–195.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Dickey, D. A. and Fuller, W. A. (1981) Likelihood ratio statistics for autoregressive time series with unit root. Econometrica, 49, 1057–1074.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Springer-Verlag, Berlin.MATHCrossRefGoogle Scholar
  8. [8]
    Ferretti, N. and Romo, J. (1996) Unit root bootstrap tests for ar(1) models. Biometrika, 83, 849–860.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Guillaume, D. M., Dacorogna, M. M., Dave, R. D., Müller, U. A., Olsen, R. B. and Pictet, O. V. (1997) From the bird’s eye to the microscope: a survey of new stylized facts of the intra-daily foreign exchange markets. Finance and Stochastics, 1, 95–129.MATHCrossRefGoogle Scholar
  10. [10]
    Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press, Princeton, NJ.MATHGoogle Scholar
  11. [11]
    Heimann, G. and Kreiss, J-P. (1996) Bootstrapping general first order autoregression. Statistics and Probability Letters, 30, 87–98.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Horváth, L. and Kokoszka, P. S. (2003) A bootstrap approximation to a unit root test statistic for heavy-tailed observations. Statistics and Probability Letters, 62, 163–173.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Jach, A. and Kokoszka, P. (2003) Subsampling unit root tests for heavy-tailed observations. Methodology and Computing in Applied Probability, 6, 73–97.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Knight, K. (1989) On the bootstrap of the sample mean in the infinite variance case. The Annals of Statistics, 17, 1168–1175.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    Ling, S. and Li, W. K. (2003) Asymptotic inference for unit root processes with GARCH(1,1) errors. Econometric Theory, 19, 541–564.MathSciNetGoogle Scholar
  16. [16]
    Ling, S. and McAleer, M. (2003) On adaptive estimation in nonstationary ARMA models with GARCH errors. Annals of Statistics, 31, 642–674.MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    Meerschaert, M. M. and Scheffler, H. P. (2001) Limit Theorems for Sums of Independent Random Vectors. Wiley, New York.Google Scholar
  18. [18]
    Paparoditis, E. and Politis, D. N. (2001) Large sample inference in the general AR(1) case. Test, 10:1, 487–589.MathSciNetGoogle Scholar
  19. [19]
    Paparoditis, E. and Politis, D. N. (2003) Residual based block bootstrap for unit root testing. Econometrica, 71:3, 813–855.MathSciNetMATHCrossRefGoogle Scholar
  20. [20]
    Politis, D. N., Romano, J. P. and Wolf, M. (1999) Subsampling. Springer-Verlag.Google Scholar
  21. [21]
    Rachev, S. and Mittnik, S. (2000) Stable Paretian Models in Finance. John Wiley & Sons Ltd.Google Scholar
  22. [22]
    Samorodnitsky, G. and Taqqu, M. S. (1994) Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall.Google Scholar
  23. [23]
    Swensen, A. R. (2003) A note on the power of bootstrap unit root tests. Econometric Theory, 19, 32–48.MathSciNetMATHCrossRefGoogle Scholar
  24. [24]
    Wang, Q., Lin, Y-X. and Gulati, C. M. (2003) Asymptotics for general fractionally integrated processes with applications to unit root tests. Econometric Theory, 19, 143–164.MathSciNetMATHCrossRefGoogle Scholar
  25. [25]
    Zarepour, M. and Knight, K. (1999) Bootstrapping unstable first order autoregressive process with errors in the domain of attraction of stable law. Communications in Statististics-Stochastic Models, 15(1), 11–27.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Piotr Kokoszka
    • 1
  • Andrejus Parfionovas
    • 1
  1. 1.Mathematics and StatisticsUtah State UniversityLogan, UtahUSA

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