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Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the accuracy of such processes as one varies the time interval of calibration and compare the performance of various types of kernels made up of sums of exponentials. Because of their around-the-clock opening times, FX markets are ideally suited to our aim as they allow us to avoid the complications of the long daily overnight closures of equity markets. One can achieve statistical significance according to three simultaneous tests provided that one uses kernels with two exponentials for fitting an hour at a time, and two or three exponentials for full days, while longer periods could not be fitted within statistical satisfaction because of the non-stationarity of the endogenous process. Fitted timescales are relatively short and endogeneity factor is high but sub-critical at about 0.8.
We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling.
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to th
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the
This paper has been withdrawn by the authors.
In this study, we have investigated factors of determination which can affect the connected structure of a stock network. The representative index for topological properties of a stock network is the number of links with other stocks. We used the mul