Robust Confidence Intervals for Autocorrelations of Stationary Time Series
Bibliographic Data
| ID | 19418436 |
|---|---|
| Authors | Tae‐Yoon Hwang (0000-0001-9397-5314, Western Kentucky University), Taeyoon Hwang (Western Kentucky University), Timothy J Vogelsang (0000-0002-8491-6715, Michigan State University, corresponding author) |
| Year | 2026 |
| Pages | 1-17 |
| Publication date | 2026-03-02 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Journal of Business and Economic Statistics (JOURNAL) |
| Journal identifiers | ISSN: 0735-0015 • E-ISSN: 1537-2707 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/07350015.2025.2561749 |
| OpenAlex | W4416171964 |
| Language | EN |
| References cited | 25 |
This paper develops a simple and new approach for testing linear hypotheses about autocorrelations for time series with general stationary serial correlation structures. A practically important special case is the computation of robust confidence intervals for individual autocorrelations that do not require resampling methods. Inference is heteroskedasticity and autocorrelation robust (HAR) and allows innovations to be uncorrelated but not necessarily independent and identically distributed (iid). It is well known that the classic Bartlett (1946) formula can provide invalid inference when innovations are not (iid). Romano and Thombs (1996) derive the asymptotic distribution of sample autocorrelations under weak assumptions but avoid estimation of the variances of sample autocorrelations and suggest resampling schemes to obtain confidence intervals. As an alternative we provide an easy to implement regression approach for estimating autocorrelations and their variance matrices. The asymptotic variance takes a sandwich form which can be estimated using well known HAR variance estimators. Resulting test statistics can be implemented with fixed-smoothing critical values which reduce finite sample size distortions. Monte Carlo simulations show our approach is robust to innovations that are not iid and works reasonably well across various serial correlation structures. An empirical illustration using robust confidence intervals for autocorrelations of S&P 500 index returns shows that conclusions about market efficiency and volatility clustering during pre and post-Covid periods using our approach contrast with conclusions using traditional (and often incorrectly used) methods. We provide a Python implementation for practitioners that implements our approach: https://eastlansing.github.io/Robust_CI_Acf
Autocorrelation · Confidence interval · Time series · Advanced Statistical Methods and Models · Financial Risk and Volatility Modeling · Statistical Methods and Inference
Modeling and Forecasting Realized Volatility
A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
A Simple Asymptotically F -Distributed Portmanteau Test for Diagnostic Checking of Time Series Models With Uncorrelated Innovations
HAR Inference
"Comment on "HAR Inference
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation
| Citation velocity | historical |
|---|---|
| Highly cited | No |