Estimating the degree of activity of jumps in high frequency data

By Yacine Aït-Sahalia, Jean Jacod. 2009

271 citations recorded by the source corpus.

We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/c3213994c33d88f89234a0a6abccac4112ef9a45

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Citations in the corpus

Nonparametric tests for pathwise properties of semimartingales (2011, methodology): “e (19) is a consequence of the independence of N and M, and of the Chebyshev inequality: as h→0, nP{∆iN 6=0 ,(∆iM)2 >crh}≤nO(h)· E[(∆iM)2] crh =O h rh . The proof of (20) can be achieved as in [3], Lemma 6, but we give a simpler proof under our assumptions. It is suﬃcient to show that P{(∆iX)2 ”
Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data (2010, methodology): “…to finite or infinite variation for X, and Todorov and Tauchen (2010), who provide a graphical method to determine whether β = 2 or β 2 using the test statistic of Aït-Sahalia and Jacod (2009b), and Belomestny (2010) who proposes a method based on low frequency historical and options data.”
Limit theorems for moving averages of discretized processes plus noise (2010, background): “Recall that the typical statistical problems in the noise-free framework are (i) estimation of the quadratic variation (see [8], [13]), (ii) tests for the presence of jumps (see [4], [9]), (iii) tests for the presence of the continuous component (see [10], [3]) or (iv) estimation of the "activity in”
Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction (2012, unknown): “For example, it is impossible to recover the entire Lévy measure μ of a discretely observed process that has both a diffusion and a jump component, even as the discretization becomes arbitrarily fine [Aı̈t-Sahalia and Jacod, 2009].”
Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation (2011, methodology): “A two-scale approach for related problems has been previously used also in [1, 24, 28].”
Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017, unknown): “We can refer to Ait-Sahalia and Jacod [1], Cont and Mancini [14]) or Todorov [39] who have demonstrated that the variance risk is manifest in two salient features of financial returns: stochastic volatility and jumps.”
Fact or friction: jumps at ultra high frequency (2014, unknown): “This line of thought is also consistent with A¨ıt-Sahalia and Jacod (2009a) who emphasize that jumps can be identiﬁed only by increasing the sampling frequency to the limit.”
Efficient estimation of integrated volatility in presence of infinite variation jumps (2014, methodology): “However, empirical results in [1] suggest that for some financial data sets jumps can be of infinite variation.”
Testing for jumps in noisy high frequency data (2012, methodology): “This conjecture is consistent with the estimates of jump activity in Aït-Sahalia and Jacod (2009a).”
On the jump activity index for semimartingales (2012, unknown): “From Ait-Sahalia and Jacod (2009b), v2(g0) = (αβ − α′β)/{At(log(α′/α))2}.”
Price jump prediction in a limit order book (2012, background): “Since then, many authors, in particular [2] have contributed to shed a better light on this phenomenon, and one can safely say that rigorous statistical tests for identifying continuous-time, real-valued processes with discontinuous paths are now available to the academic community as well as the ap”