Abstract. This paper studies a semiparametric inference procedure for a finite-dimensional parameter in a continuous-time regression model involving high-frequency data in a large cross-section. The model concerns the relationship between a noisy dependent process and a possibly nonlinear transform of stochastic volatility over a fixed time span, with its coefficients allowed to depend on a set of firm-specific characteristics. The construction of the estimator involves two steps: the nonparametric recovery of stochastic volatility processes, followed by a parametric second stage that uses the volatility estimates. I show that the estimator admits a central limit theorem and provide a consistent estimator of the asymptotic conditional variance based on a factor-analytic method. The finite sample performance of the inference procedure is satisfactory in a realistically calibrated Monte Carlo setting. In a novel empirical application, I study the relationship between bid-ask spread and the spot standard deviation of asset price. The slope coefficient estimate, which measures the heterogeneous level of information asymmetry, is closely related to firm characteristics such as size, algorithmic trading proxies, and institutional ownership.
- Variation and Efficiency of High-Frequency Betas, with Jia Li, George Tauchen and Viktor Todorov, resubmitted at Journal of Econometrics.
Abstract. This paper studies the efficient estimation of betas from high-frequency return data on a fixed time interval. Under an assumption of equal diffusive and jump betas, we derive the semiparametric efficiency bound for estimating the common beta and we develop an adaptive estimator that attains the efficiency bound. We further propose a Hausman type test for deciding whether the common beta assumption is true from the high-frequency data. In our empirical analysis we provide examples of stocks and time periods for which a common market beta assumption appears true and ones for which this is not the case. We further quantify empirically the gains from the efficient common beta estimation developed in the paper.
- Glivenko-Cantelli Theorems for Integrated Functionals of Stochastic Processes, with Jia Li and Yunxiao Liu.
Abstract. We prove a Glivenko–Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Holder classes as special cases. The general Glivenko–Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.
Publications and forthcoming papers
- Occupation Density Estimation for Noisy High-Frequency Data, with Tim Bollerslev and Jia Li, forthcoming at Journal of Econometrics.
Abstract. This paper studies the nonparametric estimation of occupation densities for semimartingale processes observed with noise. As leading examples we consider the stochastic volatility of a latent efficient price process, the volatility of the latent noise that separates the efficient price from the actually observed price, and nonlinear transformations of these processes. Our estimation methods are decidedly nonparametric and consist of two steps: the estimation of the spot price and noise volatility processes based on pre-averaging techniques and in-fill asymptotic arguments, followed by a kernel-type estimation of the occupation densities. Our spot volatility estimates attain the optimal rate of convergence, and are robust to leverage effects, price and volatility jumps, general forms of serial dependence in the noise, and random irregular sampling. The convergence rates of our occupation density estimates are directly related to that of the estimated spot volatilities and the smoothness of the true occupation densities. An empirical application involving high-frequency equity data illustrates the usefulness of the new methods in illuminating time-varying risks, market liquidity, and informational asymmetries across time and assets.
- Are Recessions Good for Government Hires? The Effect of Unemployment on Public Sector Human Capital, with John M. de Figueiredo, Economics Letters, 170, 1-5, 2018. (also NBER working paper No. 24538).