Papers

2019

1. The Fourier transform method for volatility functional inference by asynchronous observations Chen, Richard Y. preprint 2019 [Abs] [HTML] [PDF]

   We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is consistent and we provide limit distributions using irregular and asynchronous observations. When observations are synchronous, the Fourier transform method for volatility functionals attains both the optimal convergence rate and the efficient bound in the sense of Le Cam and Hájek. Another finding is asynchronicity or missing data as a form of noise produces “interference” in the spectrum estimation and impacts on the convergence rate of volatility functional estimators. This new methodology extends previous applications of volatility functionals, including principal component analysis, generalized method of moments, continuous-time linear regression models et cetera, to high-frequency datasets of which asynchronicity is a prevalent feature.

2. Volatility functionals of Itô semimartingales: microstructure noise and time-domain adaptive estimation Chen, Richard Y. work in progress 2019 [Abs]

   The time-domain smoothing for covariance matrix estimation can achieve the optimal convergence rate but does not attain the semiparametric efficiency bound established in the literature. This shortcoming of time-domain smoothing persists in volatility functional inference. This paper proposes to pre-estimate the signal-to-noise ratio and choose smoothing hyperparameter in a data-driven fashion. The phenomenon of "borrowing strength from other dimensions" is discussed. The attendant asymptotic variance lies within 7% of the semiparametric efficiency bound.

3. Reassessment of long-range dependence of volatility by the estimation of volatility spectrum using high-frequency data Chen, Richard Y. work in progress 2019 [Abs]

   The smoothness of stochastic volatility consequentially influences the applications and practice of financial time series. This paper studies the problem of measuring the roughness of volatility sample path using high-frequency observations of continuous semimartingales. The roughness measure is based on the Hurst parameter of fractional Brownian motion. The estimation procedure is conducted in frequency domain via periodogram-based regression. The consistency and the limit distributions are studied. This line of research will shed light on the spectral analysis of long-memory processes, particularly the corresponding asymptotic properties of periodograms, as well the empirical dependence range of volatility in high-frequency data.

2018

1. Inference for volatility functionals of multivariate Itô semimartingales observed with jump and noise Chen, Richard Y. preprint 2018 [Abs] [HTML] [PDF]

   This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate Itô semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correction. Estimators based on this framework achieve the optimal convergence rate. A class of stable central limit theorems are attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the continuous-time linear regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data.

2017

1. Model-free approaches to discern non-stationary market microstructure noise and time-varying liquidity in high-frequency data Chen, Richard Y., and Mykland, Per A. Journal of Econometrics 2017 [Abs] [HTML] [PDF]

   In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Itô semimartingales, and discuss how to measure liquidity risk using high-frequency financial data. In particular, we investigate the impact of non-stationary microstructure noise on some volatility estimators, and design three complementary tests by exploiting edge effects, information aggregation of local estimates and high-frequency asymptotic approximation. The asymptotic distributions of these tests are available under both stationary and non-stationary assumptions, thereby enable us to conservatively control type-I errors and meanwhile ensure the proposed tests enjoy the asymptotically optimal statistical power. Besides it also enables us to empirically measure aggregate liquidity risks by these test statistics. As byproducts, functional dependence and endogenous microstructure noise are briefly discussed. Simulation with a realistic configuration corroborates our theoretical results, and our empirical study indicates the prevalence of non-stationary microstructure noise in New York Stock Exchange.