New Economics Papers
on Market Microstructure
Issue of 2011‒12‒19
two papers chosen by
Thanos Verousis

  1. Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data By E. Bacry; K. Dayri; J. F. Muzy
  2. Asymptotic theory of range-based multipower variation By Kim Christensen; Mark Podolskij

  1. By: E. Bacry; K. Dayri; J. F. Muzy
    Abstract: We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation function is computed using a minimal phase recovering method. We illustrate our method on some examples and provide an empirical study of the estimation errors. Within this framework, we analyze high frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics.
    Date: 2011–12
  2. By: Kim Christensen (Aarhus University and CREATES); Mark Podolskij (University of Heidelberg and CREATES)
    Abstract: In this paper, we present a realised range-based multipower variation theory, which can be used to estimate return variation and draw jump-robust inference about the diffusive volatility component, when a high-frequency record of asset prices is available. The standard range-statistic – routinely used in financial economics to estimate the variance of securities prices – is shown to be biased when the price process contains jumps. We outline how the new theory can be applied to remove this bias by constructing a hybrid range-based estimator. Our asymptotic theory also reveals that when high-frequency data are sparsely sampled, as is often done in practice due to the presence of microstructure noise, the range-based multipower variations can produce significant efficiency gains over comparable subsampled returnbased estimators. The analysis is supported by a simulation study and we illustrate the practical use of our framework on some recent TAQ equity data.
    Keywords: High-frequency data, Integrated variance, Realised multipower variation, Realised range-basedmultipower variation, Quadratic variation.
    JEL: C10 C80
    Date: 2011–10–30

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