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A bootstrap-based KPSS test for functional time series

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  • Chen, Yichao
  • Pun, Chi Seng

Abstract

In this study, we examine bootstrap methods to construct a generalized KPSS test for functional time series. Bootstrap-based functional testing provides an intuitive and efficient estimation of the distribution of the generalized KPSS test statistic and is capable of achieving non-trivial powers against many alternative hypotheses. We derive the asymptotic distribution of the simple bootstrap-based KPSS test statistic for functional time series, which proves the bootstrap validity on average. Simulation studies are then conducted to examine the performance of the proposed KPSS tests in small and moderate sample sizes. The results demonstrate that the bootstrap-based functional KPSS test has good empirical size and power. Moreover, its implementation is more efficient than the existing KPSS test for functional time series.

Suggested Citation

  • Chen, Yichao & Pun, Chi Seng, 2019. "A bootstrap-based KPSS test for functional time series," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:jmvana:v:174:y:2019:i:c:s0047259x18306146
    DOI: 10.1016/j.jmva.2019.104535
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    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. Lajos Horváth & Piotr Kokoszka & Ron Reeder, 2013. "Estimation of the mean of functional time series and a two-sample problem," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 103-122, January.
    3. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    4. Han Lin Shang, 2017. "Forecasting intraday S&P 500 index returns: A functional time series approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(7), pages 741-755, November.
    5. Lee, Dongin & Schmidt, Peter, 1996. "On the power of the KPSS test of stationarity against fractionally-integrated alternatives," Journal of Econometrics, Elsevier, vol. 73(1), pages 285-302, July.
    6. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    7. 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.
    8. 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.
    9. Horváth, Lajos & Husková, Marie & Kokoszka, Piotr, 2010. "Testing the stability of the functional autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 352-367, February.
    10. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
    11. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    12. Tomasz Górecki & Siegfried Hörmann & Lajos Horváth & Piotr Kokoszka, 2018. "Testing Normality of Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(4), pages 471-487, July.
    13. Liebl, Dominik, 2013. "Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective," MPRA Paper 50881, University Library of Munich, Germany.
    14. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    15. Piotr Kokoszka & Matthew Reimherr, 2013. "Determining the order of the functional autoregressive model," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 116-129, January.
    16. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    17. Berkes, István & Horváth, Lajos & Rice, Gregory, 2013. "Weak invariance principles for sums of dependent random functions," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 385-403.
    18. E. Paparoditis & T. Sapatinas, 2016. "Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data," Biometrika, Biometrika Trust, vol. 103(3), pages 727-733.
    19. Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2010. "Tests for Error Correlation in the Functional Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1113-1125.
    20. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    21. Alexander Aue & Gregory Rice & Ozan Sönmez, 2018. "Detecting and dating structural breaks in functional data without dimension reduction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 509-529, June.
    22. Shang, Han Lin, 2017. "Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration," Econometrics and Statistics, Elsevier, vol. 1(C), pages 184-200.
    23. P. Constantinou & P. Kokoszka & M. Reimherr, 2017. "Testing separability of space-time functional processes," Biometrika, Biometrika Trust, vol. 104(2), pages 425-437.
    24. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
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