Abstract
This paper assesses the performance of tests for a single structural change at unknown date when regressors are stationary, trending and when they have a break in mean. Size and power of the test procedures are compared in a simulation setup particularly aimed at autoregressive models using their limiting distribution and some bootstrap approximations. The comparisons are performed using graphical methods, namely P value discrepancy plots and size–power curves. The simulation study gives some interesting insights to the test procedures. Indeed, it documents that tests based on the conventional asymptotic distribution are oversized in small samples. The size correction is achieved by some bootstrap methods which appear to possess reasonable size properties. For the power study, the proposed bootstrap method improves on the asymptotic approximations of some tests for heteroskedastic regression errors especially when there is a mean-shift in the regressors. This result has not been found for the case of i.i.d. errors where the bootstrap tests have the same power properties as the tests based on the asymptotic approximations. We finally study the relationship between two monthly US interest rates. The results show that such relationship has been altered by a regime-shift located in May 1981.
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References
Amemiya T (1985) Advanced econometrics. Harvard University Press, Cambridge
Andrews DWK (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61: 821–856
Andrews DWK (2003) Tests for parameter instability and structural change with unknown change point: a corrigendum. Econometrica 71: 395–397
Andrews DWK, Ploberger W (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62: 1383–1414
Andrews DWK, Lee I, Ploberger W (1996) Optimal change point tests for normal linear regression. J Econom 70: 9–38
Bai J (1997) Estimation of a change point in multiple regression models. Rev Econ Stat 79: 551–563
Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66: 47–78
Beran R (1986) Simulating power functions. Ann Stat 14: 151–173
Beran R, Srivastava MS (1985) Bootstrap tests and confidence regions for functions of a covariance matrix. Ann Stat 13: 95–115
Chow GC (1960) Tests of equality between sets of coefficients in two linear regressions. Econometrica 28: 591–605
Chu CSJ, Hornik K, Kuan CM (1995) MOSUM tests for parameter constancy. Biometrika 82: 603–617
Davidson R, Flachaire E (1999) The wild bootstrap, tamed at last. Working paper no. 99A32, GREQAM, University of Aix-Marseille II
Davidson R, MacKinnon J (1998) Graphical methods for investigating the size and power of test statistics. Manch Sch 66: 1–26
Davidson R, MacKinnon J (1999) The size distortion of bootstrap tests. Econom Theory 15: 361–376
Davidson R, MacKinnon J (2000) Bootstrap tests: how many bootstraps?. Econom Rev 19: 55–68
Davidson R, MacKinnon J (2006) The power of bootstrap and asymptotic tests. J Econom 133: 421–441
Diebold FX, Chen C (1996) Testing structural stability with endogenous break point: a size comparison of analytic and bootstrap procedures. J Econom 70: 221–241
Dwass M (1957) Modified randomization tests for nonparametric hypotheses. Ann Math Stat 28: 181–187
Efron B (1979) Bootstrap methods; another look at the Jackknife. Ann Stat 7: 1–26
Efron B (1982) The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics, Philadelphia
Hall P (1986) On the number of bootstrap simulations required to construct a confidence interval. Ann Stat 14: 1453–1462
Hall P (1992) The bootstrap and edgeworth expansion. In: Springer Series in Statistics. Springer, New York
Hansen BE (1992) Tests for parameter instability in regressions with I(1) processes. J Bus Econ Stat 10: 321–335
Hansen BE (1997) Approximate asymptotic p-values for structural change tests. J Bus Econ Stat 15: 60–67
Hansen BE (2000) Testing for structural change in conditional models. J Econom 97: 93–115
Hjort NL, Koning A (2002) Tests for constancy of model parameters over time. Nonparametr Stat 14: 113–132
Horowitz JL (1994) Bootstrap-based critical values for the information matrix test. J Econom 61: 395–411
Horowitz JL (1997) Bootstrap methods in econometrics: theory and numerical performance. In: Kreps DM, Wallis KF (eds) Advances in economics and econometrics: theory and applications, vol 3. Cambridge University Press, Cambridge, pp 188–222
Jeong J, Maddala GS (1993) A perspective on application of bootstrap methods in econometrics. In: Maddala GS, Rao CR, Vinod HD (eds) Handbook of statistics: econometrics, vol 11. McGraw-Hill, New York, pp 573–610
Jouini J, Boutahar M (2005) Evidence on structural changes in US time series. Econ Modell 22: 391–422
Liu RY (1988) Bootstrap procedure under some non-i.i.d. models. Ann Stat 16: 1696–1708
Nyblom J (1989) Testing the constancy of parameters over time. J Am Stat Assoc 84: 223–230
Quandt RE (1960) Tests of the hypothesis that a linear regression obeys two separate regimes. J Am Stat Assoc 55: 324–330
Stein H (1984) Presidential economics: the making of economic policy from Roosevelt to Reagan and beyond. Simon and Shuster, New York
White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50: 1–25
Zeileis A (2005) A unified approach to structural change tests based on ML scores, F statistics, and OLS residuals. Econom Rev 24: 445–466
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Jouini, J. Bootstrap methods for single structural change tests: power versus corrected size and empirical illustration. Stat Papers 51, 85–109 (2010). https://doi.org/10.1007/s00362-008-0123-6
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DOI: https://doi.org/10.1007/s00362-008-0123-6