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Mode Identification of Volatility in Time-Varying Autoregression

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  • Gabriel Chandler
  • Wolfgang Polonik

Abstract

In many applications, time series exhibit nonstationary behavior that might reasonably be modeled as a time-varying autoregressive (AR) process. In the context of such a model, we discuss the problem of testing for modality of the variance function. We propose a test of modality that is local and, when used iteratively, can be used to identify the total number of modes in a given series. This problem is closely related to peak detection and identification, which has applications in many fields. We propose a test that, under appropriate assumptions, is asymptotically distribution free under the null hypothesis, even though nonparametric estimation of the AR parameter functions is involved. Simulation studies and applications to real datasets illustrate the behavior of the test.

Suggested Citation

  • Gabriel Chandler & Wolfgang Polonik, 2012. "Mode Identification of Volatility in Time-Varying Autoregression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1217-1229, September.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1217-1229
    DOI: 10.1080/01621459.2012.703877
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    Cited by:

    1. Djogbenou, Antoine & Inan, Emre & Jasiak, Joann, 2023. "Time-varying coefficient DAR model and stability measures for stablecoin prices: An application to Tether," Journal of International Money and Finance, Elsevier, vol. 139(C).
    2. Valentin Patilea & Hamdi Raïssi, 2014. "Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1099-1111, September.
    3. Gabe Chandler & Wolfgang Polonik, 2017. "Residual Empirical Processes and Weighted Sums for Time-Varying Processes with Applications to Testing for Homoscedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 72-98, January.

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