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Fourier-Type Monitoring Procedures for Strict Stationarity

  • S. Lee
  • S. G. Meintanis
  • C. PretoriusEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 250)

Abstract

We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Monte Carlo results as well as an application to financial data are presented.

References

  1. 1.
    Andrews, B., Calder, M., & Davis, R. A. (2009). Maximum likelihood estimation for α-stable autoregressive processes. The Annals of Statistics, 37, 1946–1982.Google Scholar
  2. 2.
    Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59, 817–858.Google Scholar
  3. 3.
    Aue, A., Horváth, L., Hǔsková, M., & Kokoszka, P. (2006). Change-point monitoring in linear models with conditionally heteroskedastic errors. The Econometrics Journal, 9, 373–403.Google Scholar
  4. 4.
    Bai, J. (1994). Weak convergence of the sequential empirical processes of residuals in ARMA models. The Annals of Statistics, 22, 2051–2061.Google Scholar
  5. 5.
    Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco: Holden-Day.Google Scholar
  6. 6.
    Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods. New York: Springer.Google Scholar
  7. 7.
    Busetti, F., & Harvey, A. (2010). Tests of strict stationarity based on quantile indicators. Journal of Time Series Analysis, 31, 435–450.Google Scholar
  8. 8.
    Dwivedi, Y., & Subba Rao, S. (2011). A test for second order stationarity of a time series based on the discrete Fourier transform. Journal of Time Series Analysis, 32, 68–91.Google Scholar
  9. 9.
    Francq, C., & Zakoïan, J. (2012). Strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity models. Econometrica, 80, 821–861.Google Scholar
  10. 10.
    Giacomini, R., Politis, D., & White, H. (2013). A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Econometric Theory, 29, 567–589.Google Scholar
  11. 11.
    Gil-Alana, L. (2003). Testing the power of a generalization of the KPSS-tests against fractionally integrated hypotheses. Computational Economics, 22, 23–38.Google Scholar
  12. 12.
    Giraitis, L., Kokoszka, P., Leipus, R., & Teyssiére, G. (2003). Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112, 265–294.Google Scholar
  13. 13.
    Guégan, D. (2010). Non-stationary samples and meta-distribution. In A. Basu, T. Samanta, & A. Sen Gupta (Eds.), Statistical paradigms. Recent advances and reconciliations. Singapore: World Scientific.Google Scholar
  14. 14.
    Guo, S., Li, D., & Li, M. (2016). Strict stationarity testing and global robust quasi-maximum likelihood estimation of DAR models, Forthcoming. https://pdfs.semanticscholar.org/3c27/34fd9e878f65749c65aba055c5439521d5f9.pdf
  15. 15.
    Hong, Y., Wang, X., & Wang, S. (2017). Testing strict stationarity with applications to macroeconomic time series. International Economic Review, 58, 1227–1277.Google Scholar
  16. 16.
    Horváth, L. P., Kokoszka, P., & Rice, G. (2014). Testing stationarity of functional time series. Journal of Econometrics, 179, 66–82.Google Scholar
  17. 17.
    Jentsch, C., & Subba Rao, S. (2015). A test for second order stationarity of a multivariate time series. Journal of Econometrics, 185, 124–161.Google Scholar
  18. 18.
    Kapetanios, G. (2009). Testing for strict stationarity in financial variables. Journal of Banking & Finance, 33, 2346–2362.Google Scholar
  19. 19.
    Künsch, H. (1989). The jackknife and the bootstrap for general stationary observations. The Annals of Statistics, 17, 1217–1241.Google Scholar
  20. 20.
    Lahiri, S. (2003). Resampling methods for dependent data. New York: Springer.Google Scholar
  21. 21.
    Lima, L., & Neri, B. (2013). A test for strict stationarity. In V. Huynh, et al. (Eds.), Uncertainty analysis in econometrics with applications. Berlin: Springer.Google Scholar
  22. 22.
    Loretan, M., & Phillips, P. (1994). Testing the covariance stationarity of heavy-tailed time series. Journal of Empirical Finance, 1, 211–248.Google Scholar
  23. 23.
    Matteson, D. S., & James, N. A. (2014). A nonparametric approach for multiple change point analysis of multivariate data. Journal of the American Statistical Association, 109, 334–345.Google Scholar
  24. 24.
    Müller, U. (2005). Size and power of tests of stationarity in highly autocorrelated time series. Journal of Econometrics, 128, 195–213Google Scholar
  25. 25.
    Székely, G., & Rizzo, M. (2005). Hierarchical clustering via joint between-within distances: Extending Ward’s minimum variance method. Journal of Classification, 22, 151–183.Google Scholar
  26. 26.
    Xiao, Z., & Lima, L. (2007). Testing covariance stationarity. Econometric Reviews, 26, 643–667.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of StatisticsSeoul National UniversitySeoulSouth Korea
  2. 2.National and Kapodistrian University of AthensAthensGreece
  3. 3.Unit for Business Mathematics and InformaticsNorth-West UniversityPotchefstroomSouth Africa
  4. 4.Unit for Business Mathematics and InformaticsNorth-West UniversityPotchefstroomSouth Africa

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