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Testing for Strict Stationarity

Author

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  • George Kapetanios

    (Queen Mary, University of London)

Abstract

The investigation of the presence of structural change in economic and financial series is a major preoccupation in econometrics. A number of tests have been developed and used to explore the stationarity properties of various processes. Most of the focus has rested on the first two moments of a process thereby implying that these tests are tests of covariance stationarity. We propose a new test for strict stationarity, that considers the whole distribution of the process rather than just its first two moments, and examine its asymptotic properties. We provide two alternative bootstrap approximations for the exact distribution of the test statistic. A Monte Carlo study illustrates the properties of the new test and an empirical application to the constituents of the S&P 500 illustrates its usefulness.

Suggested Citation

  • George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:602
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    References listed on IDEAS

    as
    1. Zhijie Xiao & Luiz Renato Lima, 2007. "Testing Covariance Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 643-667.
    2. George Kapetanios, 2004. "The Impact of Large Structural Shocks on Economic Relationships: Evidence from Oil Price Shocks," Working Papers 524, Queen Mary University of London, School of Economics and Finance.
    3. GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," LIDAM Reprints CORE 1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Mohsen Pourahmadi, 1988. "STATIONARITY OF THE SOLUTION OF Xt= AtXt‐1+εt AND ANALYSIS OF NON‐GAUSSIAN DEPENDENT RANDOM VARIABLES," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 225-239, May.
    5. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2005. "Nonparametric estimation of time varying parameters under shape restrictions," Journal of Econometrics, Elsevier, vol. 126(1), pages 53-77, May.
    6. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
    7. Zhijie Xiao, 2001. "Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 87-105, January.
    8. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    9. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-166, April.
    10. Bart Hobijn & Philip Hans Franses & Marius Ooms, 2004. "Generalizations of the KPSS‐test for stationarity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 483-502, November.
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    Cited by:

    1. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    2. Hart, Jeffrey D., 2016. "A nonparametric test of stationarity for independent data," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 40-44.
    3. Kapetanios, George, 2009. "Testing for strict stationarity in financial variables," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2346-2362, December.

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    More about this item

    Keywords

    Covariance stationarity; Strict stationarity; Bootstrap; S&P500;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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