2021/03/02 by Alessandro Casini, Casini, Alessandro, Taosong Deng +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Engineering · #Complex Systems and Time Series Analysis #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Fault Detection and Control Systems #Financial Risk and Volatility Modeling #Forecasting Techniques and Applications #Market Dynamics and Volatility #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2103.01604
openalex publication_date 2021/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/28
We establish theoretical results about the low frequency contamination (i.e.,\nlong memory effects) induced by general nonstationarity for estimates such as\nthe sample autocovariance and the periodogram, and deduce consequences for\nheteroskedasticity and autocorrelation robust (HAR) inference. We present\nexplicit expressions for the asymptotic bias of these estimates. We distinguish\ncases where this contamination only occurs as a small-sample problem and cases\nwhere the contamination continues to hold asymptotically. We show theoretically\nthat nonparametric smoothing over time is robust to low frequency\ncontamination. Our results provide new insights on the debate between\nconsistent versus inconsistent long-run variance (LRV) estimation. Existing LRV\nestimators tend to be in inflated when the data are nonstationary. This results\nin HAR tests that can be undersized and exhibit dramatic power losses. Our\ntheory indicates that long bandwidths or fixed-b HAR tests suffer more from low\nfrequency contamination relative to HAR tests based on HAC estimators, whereas\nrecently introduced double kernel HAC estimators do not super from this\nproblem. Finally, we present second-order Edgeworth expansions under\nnonstationarity about the distribution of HAC and DK-HAC estimators and about\nthe corresponding t-test in the linear regression model.\n