ASSESSMENT OF UNCERTAINTY IN HIGH FREQUENCY DATA: THE OBSERVED ASYMPTOTIC VARIANCE

• 成果类型: Article
• 署名作者: Mykland, Per A.; Zhang, Lan
• 署名单位: University of Chicago; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA12501
• 发表日期: 2017
• 页码: 197-231
• 关键词: STOCHASTIC VOLATILITY MODELS; LOG LIKELIHOOD RATIO; ULTRA-HIGH-FREQUENCY; microstructure noise; realized volatility; COVARIATION ESTIMATION; INTEGRATED VOLATILITY; econometric-analysis; FINANCIAL ECONOMICS; BARTLETT IDENTITIES

摘要

The availability of high frequency financial data has generated a series of estimators based on intra-day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create feasible statistics for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Theta = integral theta(t) dt, where the spot parameter process. can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two-scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.