ANOVA for diffusions and Itô processes

By Per Aslak Mykland, Lan Zhang. 2006

162 citations recorded by the source corpus.

Ito processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, "ANOVA for diffusions and Ito processes," can be used to measure the statistical quality of a parametric model and, non-parametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/119c7948d362a122240bc45c209215c975851637

How researchers see this paper

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In Finance

1. Yacine Aït-Sahalia
2. V. Todorov
3. Asger Lunde
4. D. Xiu
5. N. Shephard
6. Tim Bollerslev
7. Jean Jacod
8. P. R. Hansen

Citations in the corpus

• On the number of common factors with high‐frequency data (2017, background): “Mykland & Zhang (2006) investigated regression relations between two Itô processes.”
• Statistical Properties of Microstructure Noise (2013, unknown): “See, for example, Jacod and Protter (1998), Mykland and Zhang (2006), among others.”
• Subsampling Realised Kernels (2007, background): “A hange of time does not a e t R t0 2udu but does in uen e the integratedquarti ity R t0 4udu; see e.g. Mykland and Zhang (2006).”
• Realized Volatility: A Review (2008, background): “Aït-Sahalia, Y., Mykland, P. A., Zhang, L. (2005).”
• Nonparametric Filtering of the Realised Spot Volatility: A Kernel-Based Approach (2007, unknown): “Our estimator includes as a special case the rolling window estimator proposed by Foster and Nelson (1996); see also Andreou and Ghysels (2002) and Mykland and Zhang (2003,2006).”
• Bootstrapping realized multivariate volatility measures (2010, result): “If prices are nonequidistant but synchronous, results in Mykland and Zhang (2006) show that although the asymptotic conditional variance of the realized covariation measures changes, the same variance estimators remain consistent.”
• Spot volatility estimation for high-frequency data ∗ (2008, background): “The convergence rate in Theorem 1 matches up with the orders of convergence in Mykland and Zhang (2008) in terms of bandwidth and sample size.”
• Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics (2008, background): “This is reasonable in view of Lemma 2 in Mykland and Zhang (2006).”
• Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach (2004, unknown): “[X , X ] 1⁄4 (X , X ) þ [X , X ] þ Op K n 1⁄4 (X , X ) T þ hX , X i þ Op(n )þ Op(K=n), from Proposition 1 in Mykland and Zhang (2006). Let M I t be the continuous martingale for which M n, I T 1⁄4 (X , X ) (n=Mn). The proof of Theorem 2 in Zhang et al. (2005) actually establishes that the sequence o”
• Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise (2008, result): “…likewise, to be able to derive central limit theorems for stochastically spaced data without assuming the times of measurement are independent of the underlying BSM, which is the assumption used by Phillips and Yu (2006), Mykland and Zhang (2006) and Barndorff-Nielsen and Shephard (2005).”
• Quasi-maximum likelihood estimation of volatility with high frequency data (2010, background): “An alternative argument given by Mykland and Zhang (2009) is to zero out the drift by changing probability measures.”
• Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data (2010, unknown): “Labys (2001), Barndorff-Nielsen and Shephard (2002), or Mykland and Zhang (2006, 2008) .”
• REALIZED VOLATILITY WHEN SAMPLING TIMES ARE POSSIBLY ENDOGENOUS (2013, methodology): “By a slight extension of Mykland and Zhang (2006), Phillips and Yu (2007) actually show directly that we are back to the result of Example 1.”