SMU SOE Online Lee Kong Chian Seminar in Econometrics (Nov 23-24, 2022, 2.30pm-5.30pm): Asymptotic Equivalence for Inference on the Volatility from Noisy Observations

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ASYMPTOTIC EQUIVALENCE FOR INFERENCE ON THE VOLATILITY FROM NOISY OBSERVATIONS

ABSTRACT Paper 1: Asymptotic Equivalence for Inference on the Volatility from Noisy Observations We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ and a nonstandard noise level. As an application, new rate-optimal estimators of the volatility function and simple efficient estimators of the integrated volatility are constructed. Click here to view paper 1. Paper 2: Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency is established in the Cramér-Rao sense. Main findings are that nonsynchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour. Click here to view paper 2. Paper 3: Inference on the Maximal Rank of Time-Varying Covariance Matrices Using High-Frequency Data We study the rank of the instantaneous or spot covariance matrix ΣX(t) of a multidimensional continuous semi-martingale X(t). Given high-frequency observations X(i/n), i=0,…,n, we test the null hypothesis rank(ΣX(t))≤r for all t against local alternatives where the average (r+1)st eigenvalue is larger than some signal detection rate vn. A major problem is that the inherent averaging in local covariance statistics produces a bias that distorts the rank statistics. We show that the bias depends on the regularity and a spectral gap of ΣX(t). We establish explicit matrix perturbation and concentration results that provide non-asymptotic uniform critical values and optimal signal detection rates vn. This leads to a rank estimation method via sequential testing. For a class of stochastic volatility models, we determine data-driven critical values via normed p-variations of estimated local covariance matrices. The methods are illustrated by simulations and an application to high-frequency data of U.S. government bonds. Click here to view paper 3. Click here to view the CV.		This seminar will be held virtually via Zoom. A confirmation email with the Zoom details will be sent to the registered email by 22 November 2022.
		PRESENTER Markus Reiss Humbodt University
		RESEARCH FIELDS Nonparametric Statistics Statistics for Stochastic Processes Statistical Inverse Problems Stochastic (Partial) Differential Equations Applications in Econometrics, Biophysics, Finance and Medical Imaging
		DATE: 23 November 2022 (Wednesday) 24 November 2022 (Thursday)
		TIME: 2.30pm - 5.30pm

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