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Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models
Alessandro Casini,David Pouvreau +1 more
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TLDR
In this paper, a double kernel HAC (DK-HAC) estimator is proposed for heteroskedasticity and autocorrelation robust (HAR) inference when data may not satisfy second-order stationarity.Abstract:
We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may arise either from parameter variation or model misspecification. In such a context, the theories that support HAR inference are either not applicable or do not provide accurate approximations. HAR tests standardized by existing long-run variance estimators then may display size distortions and little or no power. This issue can be more severe for methods that use long bandwidths (i.e., fixed-b HAR tests). We introduce a class of nonstationary processes that have a time-varying spectral representation which evolves continuously except at a finite number of time points. We present an extension of the classical heteroskedasticity and autocorrelation consistent (HAC) estimators that applies two smoothing procedures. One is over the lagged autocovariances, akin to classical HAC estimators, and the other is over time. The latter element is important to flexibly account for nonstationarity. We name them double kernel HAC (DK-HAC) estimators. We show the consistency of the estimators and obtain an optimal DK-HAC estimator under the mean squared error (MSE) criterion. Overall, HAR tests standardized by the proposed DK-HAC estimators are competitive with fixed-b HAR tests, when the latter work well, with regards to size control even when there is strong dependence. Notably, in those empirically relevant situations in which previous HAR tests are undersized and have little or no power, the DK-HAC estimator leads to tests that have good size and power.read more
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Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series
Pavel Cizek,Chao Koo +1 more
TL;DR: In this paper, a varying-coefficient model is proposed for time series with heteroskedastic and serially correlated errors, where the conditional error variance is allowed to exhibit discontinuities at a finite set of points.
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Backward CUSUM for Testing and Monitoring Structural Change
Sven Otto,Jörg Breitung +1 more
TL;DR: Two alternative detector statistics are proposed: the backward CUSUM detector sequentially cumulates the recursive residuals in reverse chronological order, whereas the stacked backward C USUM detector considers a triangular array of backward cumulated residuals.
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Change-Point Analysis of Time Series with Evolutionary Spectra
Alessandro Casini,Pierre Perron +1 more
TL;DR: In this article, a change-point method for the spectrum of a locally stationary time series is proposed. But the method is limited to series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less smooth under the alternative.
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The Fixed-b Limiting Distribution and the ERP of HAR Tests Under Nonstationarity
TL;DR: In this article, the authors show that the nonstandard limiting distribution of HAR test statistics under fixed-b asymptotics is not pivotal (even after studentization) when the data are nonstationarity.
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Structural breaks in Box-Cox transforms of realized volatility: a model selection perspective
TL;DR: This work draws upon the fact that the HAR model is a constrained AR model and cast the problem of estimating structural breaks in the autoregressive volatility dynamics as a model selection problem, and finds the number of breaks to be heavily influenced by Box-Cox transformations applied to realized volatility series of eight stock market indices.
References
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A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix
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TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
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The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis
TL;DR: In this paper, the authors consider the null hypothesis that a time series has a unit root with possibly nonzero drift against the alternative that the process is "trend-stationary" and show how standard tests of the unit root hypothesis against trend stationary alternatives cannot reject the unit-root hypothesis if the true data generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break.
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Comparing Predictive Accuracy
TL;DR: In this article, explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts are proposed and evaluated, and asymptotic and exact finite-sample tests are proposed, evaluated and illustrated.