High-Frequency Instruments and Identification-Robust Inference for Stochastic Volatility Models

Abstract

We introduce a novel class of stochastic volatility models, which can utilize and relate many high-frequency realized volatility (RV) measures to latent volatility. Instrumental variable methods provide a unified framework for estimation and testing. We study parameter inference problems in the proposed framework with nonstationary stochastic volatility and exogenous predictors in the latent volatility process. Identification-robust methods are developed for a joint hypothesis involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For inference about the volatility persistence parameter, projection techniques are applied. The proposed tests include Anderson-Rubin-type tests and their point-optimal versions. For distributional theory, we provide finite-sample tests and confidence sets for Gaussian errors, establish exact Monte Carlo test procedures for non-Gaussian errors (possibly heavy-tailed), and show asymptotic validity under weaker assumptions. Simulation results show that the proposed tests outperform the asymptotic test regarding size and exhibit excellent power in empirically realistic settings. The proposed inference methods are applied to IBM's price and option data (2009–2013). We consider 175 different instruments (IVs) spanning 22 classes and analyze their ability to describe the low-frequency volatility. IVs are compared based on the average length of the proposed identification-robust confidence intervals. The superior instrument set mostly comprises 5-min HF realized measures, and these IVs produce confidence sets which show that the volatility process is nearly unit-root. In addition, we find RVs with higher frequency yield wider confidence intervals than RVs with slightly lower frequency, indicating that these confidence intervals adjust to absorb market microstructure noise. Furthermore, when we consider irrelevant or weak IVs (jumps and signed jumps), the proposed tests produce unbounded confidence intervals. We also find that both RV and BV measures produce almost identical confidence intervals across all 14 subclasses, confirming that our methodology is robust in the presence of jumps. Finally, although jumps contain little information regarding the low-frequency volatility, we find evidence that there may be a nonlinear relationship between jumps and low-frequency volatility.