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Testing Strict Stationarity With Applications To Macroeconomic Time Series

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  • Yongmiao Hong
  • Xia Wang
  • Shouyang Wang

Abstract

We propose a model†free test for strict stationarity. The idea is to estimate a nonparametric time†varying characteristic function and compare it with the empirical characteristic function based on the whole sample. We also propose several derivative tests to check time†invariant moments, weak stationarity, and pth order stationarity. Monte Carlo studies demonstrate excellent power of our tests. We apply our tests to various macroeconomic time series and find overwhelming evidence against strict and weak stationarity for both level and first†differenced series. This suggests that the conventional time series econometric modeling strategies may have room to be improved by accommodating these time†varying features.

Suggested Citation

  • Yongmiao Hong & Xia Wang & Shouyang Wang, 2017. "Testing Strict Stationarity With Applications To Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1227-1277, November.
    • Handle: RePEc:wly:iecrev:v:58:y:2017:i:4:p:1227-1277
    DOI: 10.1111/iere.12250
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    Cited by:

    1. Shichao Du & Chin-Han Chan, 2023. "Baby Boom or Baby Bust After the COVID-19 Onset in the United States? Evidence from an ARIMA Time-Series Analysis," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 42(6), pages 1-22, December.
    2. 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).
    3. Sun, Yuying & Hong, Yongmiao & Wang, Shouyang & Zhang, Xinyu, 2023. "Penalized time-varying model averaging," Journal of Econometrics, Elsevier, vol. 235(2), pages 1355-1377.
    4. 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.
    5. Fu, Zhonghao & Hong, Yongmiao, 2019. "A model-free consistent test for structural change in regression possibly with endogeneity," Journal of Econometrics, Elsevier, vol. 211(1), pages 206-242.
    6. Fu, Zhonghao & Hong, Yongmiao & Su, Liangjun & Wang, Xia, 2023. "Specification tests for time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 235(2), pages 720-744.
    7. Xiaojun Song & Haoyu Wei, 2021. "Nonparametric Tests of Conditional Independence for Time Series," Papers 2110.04847, arXiv.org.
    8. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2021. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 224(2), pages 306-329.

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