Realized range-based estimation of integrated variance

By Kim Christensen, Mark Podolskij. 2007

251 citations recorded by the source corpus.

We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with realized range-based variance - a statistic that replaces every squared return of realized variance with a normalized squared range. If the entire sample path of the process is available, and under a set of weak conditions, our statistic is consistent and has a mixed Gaussian limit, whose precision is five times greater than that of realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to get a consistent, mixed normal estimator, irrespective of non-trading effects. This estimator has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the high-low. The methodology is applied to TAQ data and compared with realized variance. Our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range-based variance.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dba5e5f05ced3a1eecd46b4d9f5bd6fcf75e446f

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Citations in the corpus

Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns (2010, background): “…have more idiosyncratic return and volatility movements and have much higher volatility in 3 Alternative non-parametric high-frequency data-based tests for jumps have recently been developed by Jiang and Oomen (2008), Mancini (2005), Christensen and Podolski (2007), and Lee and Mykland (2008).”
Exponential GARCH Modeling With Realized Measures of Volatility (2016, unknown): “…estimator by Zhang, Mykland, and A¨ıt-Sahalia (2005) and Zhang (2006), respectively, the realized kernel by Barndorff-Nielsen et al. (2008), the realized range by Christensen and Podolskij (2007), see also Andersen, Dobrev, and Schaumburg (2008), Hansen and Horel (2009), and references therein.”
Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps (2007, methodology): “In principle, it is possible to test for jumps in the noisy model by comparing the multiscale estimator or the realised kernel estimator with the robust statistic MBV (Z, 1, 1)n (see, for instance, Barndorff-Nielsen & Shephard [10] or Christensen & Podolskij [16] for more details on such tests in th”
Volatility Forecast Comparison Using Imperfect Volatility Proxies (2006, unknown): “10 Analytical and empirical results on the range and ‘‘realised range’’ under more flexible DGPs are presented in two recent papers by Christensen and Podolskij (2007) and Martens and van Dijk (2007). 11 When the DGP is specified to be log-normal or GARCH stochastic volatility diffusions, Patton and”
Optimal combinations of realised volatility estimators (2009, methodology): “Our fifth type of realised measure is the “realised range-based variance” (R RV ) of Christensen and Podolskij (2007) and Martens and van Dijk (2007).”
Does Anything Beat 5-Minute RV? A Comparison of Realized Measures Across Multiple Asset Classes (2015, unknown): “Correspondingly, Christensen and Podolskij (2007) and Martens and Van Dijk (2007) apply the same arguments to intraday data, and improve on the RV estimator by replacing each intraday squared return with the high-low range from a block of intra-day returns.”
A Note on the Central Limit Theorem for Bipower Variation of General Functions. (2008, methodology): “…of X. Asymptotic properties of realised bipower variation have been used to construct tests for jumps (see Barndorff-Nielsen & Shephard (2006), Christensen & Podolskij (2006b) or Ait-Sahalia & Jacod (2006)) or to provide goodness-of-fit tests for the parametric form of the volatility function…”
Realising the future: forecasting with high frequency based volatility (HEAVY) models (2010, unknown): “E-mail: neil.shephard@economics.ox.ac.uk 1 See also the work by Bandi and Russell (2006, 2008), Andersen et al. (2006), Hansen and Lunde (2006), Corradi and Distaso (2006) and Christensen and Podolskij (2007).”
Data-based ranking of realised volatility estimators (2011, methodology): “Finally, I consider the ‘‘realised range-based variance’’ (RRV) of Christensen and Podolskij (2007) and Martens and van Dijk (2007). I use 5-min blocks, as in Christensen and Podolskij (2007), with 1-min prices within each block. I compare these estimators with RV based on calendar-time trade prices”
Comparison of Volatility Measures: A Risk Management Perspective (2010, unknown): “t next to the log-high and log-close; Christensen and Podolskij (2007) develop the asymptotic theory”
Evaluating Volatility and Correlation Forecasts (2009, background): “Christensen and Podolskij show that this adjustment factor leads to an asymptotically unbiased proxy for general Brownian semi-martingales (as the number of intra-daily observations, m , goes to infinity, see [17]).”
Forecasting the realized range-based volatility using dynamic model averaging approach (2017, unknown): “…realized range-based volatility (RRV) and the realized range-based bi-power variation (RBV) are specified as below (Christensen and Podolskij, 2006; Christensen and Podolskij, 2007): ∫ ∑RRV σ s ds λ k s→ ( ) + 1 ( ).t m t m s t , ∆ 0 2 2, 0< ≤ 2 (3) ∫∑RBV λ s s σ s ds= 1 * * → ( ) .t m m j t j Δ…”