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Author: Admin | 2025-04-28
Rates using GPUs [11]. This clearly indicates that there is interest in very fast Hawkes calibration.Some even more recent research [1], published last month, by Fonseca and Zaatour, describes fast calibration without evaluating the likelihood function. Instead, the authors use Generalised Method of Moments to estimate the parameter values. They show how to compute, in closed-form, moments of any order and autocorrelation of the number of jumps within a given time interval. While not as accurate as MLE, the GMM seems to provide an "immediate" (in the words of the authors) estimation. No comparison in speeds is provided but from what I understood all that is required is to calculate the empirical autocorrelation over a number of time lags and to minimise the objective function.ConclusionIn this article I showed that a Hawkes process is a good model for explaining the clustered arrival of Mtgox trades. I showed how to estimate and evaluate a model given trade timestamps and highlighted some of the issues around estimation.Bitcoin exchange data and its price discovery has not been studied well (or at all?) yet. Self-exciting models might answer questions such as how much of Bitcoin price movements are due to fundamental events, or how much is a result of lots of reactionary algorithms hooked up on Mtgox's API. The model itself could naturally be also part of a trading strategy.You can get the data and code to reproduce the graphs and results from this repository.References[1] J. Fonseca, and R. Zaatour: Hawkes Process: Fast Calibration, Application to Trade Clustering and Diffusive Limit ssrn.[2] P. Hewlett: Clustering of order arrivals, price impact and trade path optimisation pdf.[3] J. Carlsson, M. Foo, H. Lee, H. Shek: High Frequency Trade Prediction with Bivariate Hawkes Process.[4] F. Lorenzen: Analysis of Order Clustering Using High Frequency Data: A Point Process Approach pdf.[5] E. Lewis, G. Mohler, P. Brantingham, and A. Bertozzi: Self-Exciting Point Process Models of Civilian Deaths in Iraq pdf.[6] P. Reynaud-Bouret, C. Tuleau-Malot, V, Rivoirard, and F. Grammont: Spike trains as (in)homogeneous Poisson processes or Hawkes processes: non-parametric adaptive estimation and goodness-of-fit tests pdf.[7] R.D. Peng: Applications of Multi-dimensional Point Process Methodology to Wildfire Hazard Assessment.[8] G.O. Mohler, M.B. Short, P.J. Brantingham, F.P. Schoenberg, and G.E. Tita: Self-Exciting Point Process Modeling of Crime pdf.[9] R.D. Peng: Multi-dimensional Point Process Models in R pdf.[10] V. Filimonov, and D. Sornette: Apparent criticality and calibration issues in the Hawkes self-excited point
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