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Seasonal Unit Root Tests for Trending and Breaking Series with Application to Industrial Production

Author

Listed:
  • Westerlund, Joakim

    (Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Costantini, Mauro

    (University of Vienna)

  • Narayan, Paresh

    (Deakin University)

  • Popp, Stephan

    (University of Duisburg–Essen)

Abstract

Some unit root testing situations are more difficult than others. In the case of quarterly industrial production there is not only the seasonal variation that needs to be considered but also the occasionally breaking linear trend. In the current paper we take this as our starting point to develop three new seasonal unit root tests that allow for a break in both the seasonal mean and linear trend of a quarterly time series. The asymptotic properties of the tests are derived and investigated in small-samples using simulations. In the empirical part of the paper we consider as an example the industrial production of 13 European countries. The results suggest that for most of the series there is evidence of stationary seasonality around an otherwise nonseasonal unit root.

Suggested Citation

  • Westerlund, Joakim & Costantini, Mauro & Narayan, Paresh & Popp, Stephan, 2009. "Seasonal Unit Root Tests for Trending and Breaking Series with Application to Industrial Production," Working Papers in Economics 377, University of Gothenburg, Department of Economics.
    • Handle: RePEc:hhs:gunwpe:0377
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    File URL: http://hdl.handle.net/2077/21047
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    References listed on IDEAS

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    1. Perron, Pierre & Vogelsang, Timothy J., "undated". "Level Shifts and Purchasing Power Parity," Instructional Stata datasets for econometrics levshift, Boston College Department of Economics.
    2. Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-335.
    3. Smith, Jeremy & Otero, Jesus, 1997. "Structural breaks and seasonal integration," Economics Letters, Elsevier, vol. 56(1), pages 13-19, September.
    4. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, January.
    5. repec:bla:obuest:v:63:y:2001:i:5:p:535-58 is not listed on IDEAS
    6. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    7. Philip Hans Franses & Timothy J. Vogelsang, 1998. "On Seasonal Cycles, Unit Roots, And Mean Shifts," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 231-240, May.
    8. Nasseh, Alireza & Strauss, Jack, 2000. "Stock prices and domestic and international macroeconomic activity: a cointegration approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 40(2), pages 229-245.
    9. 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.
    10. Artur C. B. da Silva Lopes & Antonio Montanes, 2005. "The Behavior Of Hegy Tests For Quarterly Time Series With Seasonal Mean Shifts," Econometric Reviews, Taylor & Francis Journals, vol. 24(1), pages 83-108.
    11. 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.
    12. Junsoo Lee & Mark C. Strazicich, 2001. "Break Point Estimation and Spurious Rejections With Endogenous Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 535-558, December.
    13. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, January.
    14. Harvey, David I. & Leybourne, Stephen J. & Newbold, Paul, 2002. "Seasonal unit root tests with seasonal mean shifts," Economics Letters, Elsevier, vol. 76(2), pages 295-302, July.
    15. David G. Fernandez, 1997. "Breaking Trends And The Money-Output Correlation," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 674-679, November.
    16. Osborn, Denise R. & Heravi, Saeed & Birchenhall, C. R., 1999. "Seasonal unit roots and forecasts of two-digit European industrial production," International Journal of Forecasting, Elsevier, vol. 15(1), pages 27-47, February.
    17. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-470, October.
    18. Binswanger, Mathias, 2004. "Stock returns and real activity in the G-7 countries: did the relationship change during the 1980s?," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 237-252, May.
    19. Popp, Stephan, 2007. "Modified seasonal unit root test with seasonal level shifts at unknown time," Economics Letters, Elsevier, vol. 97(2), pages 111-117, November.
    20. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
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    More about this item

    Keywords

    Seasonal unit root tests; Structural breaks; Linear time trend; Industrial production;
    All these keywords.

    JEL classification:

    • 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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