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Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models

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The literature on heteroskedasticity and autocorrelation robust (HAR) inference is extensive but its usefulness relies on stationarity of the relevant process, say Vt, usually a function of the data and estimated model residuals. Yet, a large body of work shows widespread evidence of various forms of nonstationarity in the latter. Also, many testing problems are such that Vt is stationary under the null hypothesis but nonstationary under the alternative. In either case, the consequences are possible size distortions and, especially, a reduction in power which can be substantial (e.g., non-monotonic power), since all such estimates are based on weighted sums of the sample autocovariances of Vt, which are inflated. We propose HAR inference methods valid under a broad class of nonstationary processes, labelled Segmented Local Stationary, which possess a spectrum that varies both over frequencies and time. It is allowed to change either slowly and continuously and/or abruptly at some time points, thereby encompassing most nonstationary models used in applied work. We introduce a double kernel estimator (DK-HAC) that applies a smoothing over both lagged autocovariances and time. The optimal kernels and bandwidth sequences are derived under a mean-squared error criterion. The data-dependent bandwidths rely on the \plug-in" approach using approximating parametric models having time-varying parameters estimated with standard methods applied to local data. Our method yields tests with good size and power under both stationary and nonstationary, thereby encompassing previous methods. In particular, the power gains are achieved without notable size distortions, the exact size being as good as those delivered by the best fixed-b approach, when the latter works well.

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  • Alessandro Casini, 2022. "Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models," CEIS Research Paper 539, Tor Vergata University, CEIS, revised 11 Apr 2022.
  • Handle: RePEc:rtv:ceisrp:539
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    3. Rainer Dahlhaus & Liudas Giraitis, 1998. "On the Optimal Segment Length for Parameter Estimates for Locally Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(6), pages 629-655, November.
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    More about this item

    Keywords

    Fixed-b; HAC standard errors; HAR; Long-run variance; Nonstationarity; Misspecification; Outliers; Segmented locally stationary.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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