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Structural Changes and Unit Roots: Distinguishing Models of Nonstationary Time Series

Author

Listed:
  • Brodsky, Boris

    () (CEMI RAS, Moscow, Russia)

Abstract

The problem of testing the hypothesis of stochastic nonstationarity (structural changes, unit roots) in univariate time series is studied in the paper. A new method of distinguishing between hypotheses of an unknown point of structural break and a unit root is proposed and its properties in the case of dependent observations are studied. The theorem of convergence to zero of the probability of accepting the false hypothesis with the sample size going to the infinity has been proved. Then the method is further analyzed in computer simulations of samples of dependent observations. Finally, applications of the method to econometric time series are considered.

Suggested Citation

  • Brodsky, Boris, 2008. "Structural Changes and Unit Roots: Distinguishing Models of Nonstationary Time Series," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 11(3), pages 52-63.
  • Handle: RePEc:ris:apltrx:0121
    as

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    References listed on IDEAS

    as
    1. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    3. 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.
    4. 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.
    5. Montañés, Antonio & Reyes, Marcelo, 2000. "Structural breaks, unit roots and methods for removing the autocorrelation pattern," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 401-409, July.
    6. 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.
    7. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    8. 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.
    9. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    10. Rappoport, Peter & Reichlin, Lucrezia, 1989. "Segmented Trends and Non-stationary Time Series," Economic Journal, Royal Economic Society, vol. 99(395), pages 168-177, Supplemen.
    11. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    12. Montañés, Antonio & Reyes, Marcelo, 1999. "The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 81-89, March.
    13. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics.
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    More about this item

    Keywords

    structural change; non-stationary time series;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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