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Tests of strict stationarity based on quantile indicators

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  • Fabio Busetti
  • Andrew Harvey

Abstract

Quantiles provide a comprehensive description of the properties of a variable, and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how departures from strict stationarity can be detected using stationarity tests based on weighted quantile indicators. Corresponding tests based on expectiles are also proposed; these might be expected to be more powerful for distributions that are not heavy‐tailed. Tests for changing dispersion and asymmetry may be based on contrasts between particular quantiles or expectiles. An overall test of the null hypothesis of strict stationarity can be constructed using the indicators from a range of quantiles. Residuals from fitting a time‐varying level or trend may be used to construct tests for relative time invariance. Empirical examples, using stock returns and US inflation, demonstrate the practical value of the tests.

Suggested Citation

  • Fabio Busetti & Andrew Harvey, 2010. "Tests of strict stationarity based on quantile indicators," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 435-450, November.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:6:p:435-450
    DOI: 10.1111/j.1467-9892.2010.00676.x
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    References listed on IDEAS

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    Cited by:

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    2. Hart, Jeffrey D., 2016. "A nonparametric test of stationarity for independent data," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 40-44.
    3. 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.
    4. Fabio Busetti, 2012. "On detecting end-of-sample instabilities," Temi di discussione (Economic working papers) 881, Bank of Italy, Economic Research and International Relations Area.
    5. Fabio Busetti & Michele Caivano & Lisa Rodano, 2015. "On the conditional distribution of euro area inflation forecast," Temi di discussione (Economic working papers) 1027, Bank of Italy, Economic Research and International Relations Area.
    6. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Fabio Busetti & Michele Caivano & Davide Delle Monache, 2021. "Domestic and Global Determinants of Inflation: Evidence from Expectile Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(4), pages 982-1001, August.
    8. Palandri, Alessandro, 2024. "Reconciling interest rates evidence with theory: Rejecting unit roots when the HD(1) is a competing alternative," Journal of Banking & Finance, Elsevier, vol. 161(C).
    9. Denys Pommeret & Laurence Reboul & Anne-francoise Yao, 2023. "Testing the equality of the laws of two strictly stationary processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 193-214, April.

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