Volatility Estimation and Jump Testing via Realized Information Variation

Abstract

We put forward a new method to construct jump‐robust estimators of integrated volatility, namely realized information variation (RIV) and realized information power variation (RIPV). The ‘information’ here refers to the difference between two‐grid of ranges in high‐frequency intervals, which preserves continuous variation and eliminates jump variation asymptotically. We show that such kind of estimators have several superior statistical properties, i.e., the estimators are generally more efficient with sufficiently using the opening, high, low, closing (OHLC) data in high‐frequency intervals, and have faster jump convergence rate due to a new type of construction. For example, the RIV is much more efficient than the estimators that only use closing prices or ranges, and the RIPV has faster jump convergence rate at Op(1/n), while the other (multi)power‐based estimators are usually Opfalse(1false/nfalse). We also extend our results to integrated quarticity and higher‐order variation estimation, and then propose the corresponding jump testing method. Simulation studies provide extensive evidence on the finite sample properties of our estimators and tests, comparing with alternative prevalent methods. Empirical results further demonstrate the practical relevance and advantages of our method.

Testing the volatility jumps based on the high frequency data

“…The wide availability of financial high frequency data has prompted the development of methodologies to test the specification of suitable models for these data. As to testing for jumps of price, the methods include the comparison of the transition density and its non‐parametric estimator (Aït‐Sahalia, 2002), the difference between power variation and multipower variation (Barndorff‐Nielsen and Shephard, 2004; 2006; Dovonon et al 2019), the ratio of power variations with different sampling frequencies (Aït‐Sahalia and Jacod, 2009; Fan and Fan, 2011), the standard return (Lee and Mykland, 2008), the difference between realized range‐based volatilities for two different sub‐splits (Liu and Wang, 2019). In reality, the observed financial data usually has microstructure noise due to the price discretization, bid‐ask spread, and so on.…”