An Estimating Equation Approach for Robust Confidence Intervals for Autocorrelations of Stationary Time Series (with Timothy J. Vogelsang)
Abstract: This paper develops an estimating equation approach to construct confidence intervals for autocorrelations for time series with general stationary serial correlation structures. Inference is heteroskedasticity and autocorrelation robust (HAR). It is well known that the Bartlett formula by Bartlett (1946) can provide invalid inference when innovations are not independent and identically distributed (i.i.d.). Romano and Thombs (1996) derive the asymptotic distribution of sample autocorrelations under weak assumptions although they avoid estimation of the variances of sample autocorrelations and use resampling schemes to obtain confidence intervals. As an alternative we provide easy to implement estimating equation approach for estimating autocorrelations and their variances. The asymptotic variances take sandwich forms which can be estimated using well known HAR variance estimators. Resulting t-statistics can be implemented with fixed-smoothing critical values. Confidence intervals using null imposed variance estimators are included in the analysis. Monte Carlo simulations show our approach is robust to innovations that are not i.i.d. and works reasonably well across various serial correlation structures. We confirmed that using fixed-smoothing critical values provides size improvements especially in small samples. Consistent with Lazarus, Lewis, Stock and Watson (2018) we find that imposing the null when estimating the asymptotic variance can reduce finite sample size distortions. An empirical illustration using 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.
Some Fixed-b Results for Regressions with High Frequency Data over Long Spans (with Timothy J. Vogelsang)
(Revision requested, Journal of Econometrics) [Paper Link]
Abstract: This paper develops fixed-b asymptotics results for heteroskedasticity autocorrelation robust (HAR) Wald tests for high frequency data using the continuous time framework of Chang, Lu and Park (2021) (CLP). It is shown that the fixed-b limit of HAR Wald tests for high frequency stationary regressions is the same as the standard fixed-b limit in Kiefer and Vogelsang (2005). For the case of cointegrating regression the form of the fixed-b limits are different from the stationary case and may or may not be pivotal. A simulation study using Ornstein-Uhlenbeck processes shows that fixed-b critical values provide rejection probabilities closer to nominal levels than traditional chi-square critical values when using data-dependent bandwidths. The Andrews (1991) data-dependent method works reasonably well for a wider range of persistence parameters than those considered by CLP. In contrast, the Newey and West (1994) data-dependent method is sensitive to the choice of pre-tuning parameters. The data-dependent method of Sun, Phillips and Jin (2008) give results similar to the Andrews (1991) method with slightly less over-rejection problems when used with fixed-b critical values. Regardless of the bandwidth method used in practice, it is clear that fixed-b critical values should be used for high frequency data. As an empirical illustration, we provide some basic empirical results on the uncovered interest parity (UIP) puzzle by using JPY/USD exchange rate return and 2-year/10-year government bond yields of US and Japan from 1991/01/02 to 2022/11/01. The empirical application shows that for some bandwidth rules, the evidence for the UIP hypothesis depends on whether normal or fixed-b critical values are used.
Works in progress
The Distribution of Realized US Corporate Bond Return Volatility
Abstract: I investigate the distribution of realized US corporate bond return volatility using the method of realized volatility (RV) introduced in Andersen et al (2001). As the corporate bond price is illiquid and irregular, I model the price dynamics of the bond using compound Poisson process. By showing that the sum of squared term of jumps in a day converges to daily integrated volatility (IV) as the number of jumps grows, I show that RV is a consistent estimator for IV in compound Poisson process set up. Monte Carlo simulation shows that as the mean of numbers of intraday price jump grows for the process, RV has smaller MAPE for estimating IV under the volatility structure following Heston model. For empirical analysis, I build series of daily realized volatilities for US corporate bonds from year 2013 to 2018 by using high frequency corporate bond transaction data (recorded every second) of Trade Reporting and Compliance Engine (TRACE) of Financial Industry Regulatory Authority (FINRA) to examine the distribution of the volatilities. The conditional distributions of volatility of US corporate bonds given the specific bond characteristics such as credit rating, issued amount, and yield exhibit distinct distributional aspects, with existence of long memory property. I also find that when there is a sizable shock to US stock market, the conditional distributions of volatility of US corporate bond have fatter tails.