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Localized level crossing random walk test robust to the presence of structural breaks

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  • Alexeev, Vitali
  • Maynard, Alex

Abstract

A modified version of the nonparametric level crossing random walk test is proposed, in which the crossing level is determined locally. This modification results in a test that is robust to unknown multiple structural breaks in the level and slope of the trend function under both the null and alternative hypotheses. No knowledge regarding the number or timing of the breaks is required. An algorithm is proposed to select the degree of localization in order to maximize bootstrapped power in a proximate model. A computational procedure is then developed to adjust the critical values for the effect of this selection procedure by replicating it under the null hypothesis. The test is applied to Canadian nominal inflation and nominal interest rate series with implications for the Fisher hypothesis.

Suggested Citation

  • Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3322-3344
    DOI: 10.1016/j.csda.2010.06.026
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    1. Ho, Hwai-Chung & Sun, Tze-Chien, 1987. "A central limit theorem for non-instantaneous filters of a stationary Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 144-155, June.
    2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    3. Evans, Martin D D & Lewis, Karen K, 1995. "Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?," Journal of Finance, American Finance Association, vol. 50(1), pages 225-253, March.
    4. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    5. Hodgson, Douglas J & Vorkink, Keith P, 2003. "Efficient Estimation of Conditional Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 269-283, April.
    6. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
    7. Hidetaka I. Ohara, 1999. "A Unit Root Test With Multiple Trend Breaks: A Theory and an Application to US and Japanese Macroeconomic Time-Series," The Japanese Economic Review, Japanese Economic Association, vol. 50(3), pages 266-290, September.
    8. Perron, Pierre & Vogelsang, Timothy J., "undated". "Level Shifts and Purchasing Power Parity," Instructional Stata datasets for econometrics levshift, Boston College Department of Economics.
    9. García, Ana & Sansó, Andreu, 2006. "A Generalization Of The Burridge–Guerre Nonparametric Unit Root Test," Econometric Theory, Cambridge University Press, vol. 22(4), pages 756-761, August.
    10. Frank Atkins & Milanda Chan, 2004. "Trend breaks and the fisher hypothesis in canada and the United States," Applied Economics, Taylor & Francis Journals, vol. 36(17), pages 1907-1913.
    11. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    13. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    14. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234, September.
    15. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    16. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639.
    17. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
    18. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    19. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    20. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    21. George Kapetanios, 2005. "Unit‐root testing against the alternative hypothesis of up to m structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 123-133, January.
    22. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    23. Mishkin, Frederic S., 1992. "Is the Fisher effect for real? : A reexamination of the relationship between inflation and interest rates," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 195-215, November.
    24. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    25. Vogelsang, T.J., 1994. "On Testing for a Unit Root in the Presence of Additive Outliers," Papers 94-30, Cornell - Department of Economics.
    26. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-320, July.
    27. Molana, H, 1991. "The Time Series Consumption Function: Error Correction, Random Walk and the Steady-State," Economic Journal, Royal Economic Society, vol. 101(406), pages 382-403, May.
    28. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
    29. Tanaka, Minoru & Shimizu, Kunio, 2001. "Discrete and continuous expectation formulae for level-crossings, upcrossings and excursions of ellipsoidal processes," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 225-232, April.
    30. Pierre Perron, 1994. "Trend, Unit Root and Structural Change in Macroeconomic Time Series," Palgrave Macmillan Books, in: B. Bhaskara Rao (ed.), Cointegration, chapter 4, pages 113-146, Palgrave Macmillan.
    31. Bryan W. Brown & Douglas J. Hodgson, 2007. "Semiparametric efficiency bounds in dynamic non-linear systems under elliptical symmetry," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 35-48, March.
    32. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    33. Zhao, Zhibiao & Wu, Wei Biao, 2007. "Asymptotic theory for curve-crossing analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 862-877, July.
    34. Burridge, Peter & Guerre, Emmanuel, 1996. "The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test," Econometric Theory, Cambridge University Press, vol. 12(4), pages 705-723, October.
    35. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    36. George Kapetanios, 2005. "Unit‐root testing against the alternative hypothesis of up to m structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 123-133, January.
    37. Heon Jin Park & Wayne A. Fuller, 1995. "Alternative Estimators And Unit Root Tests For The Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 415-429, July.
    38. Tailen Hsing, 2000. "Linear Processes, Long-Range Dependence and Asymptotic Expansions," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 19-29, January.
    39. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    40. Felipe Aparicio & Alvaro Escribano & Ana E. Sipols, 2006. "Range Unit‐Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 545-576, July.
    41. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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    More about this item

    Keywords

    Level crossing; Random walk; Structural breaks; Unit root; Robustness;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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