Most fits of Hawkes processes in financial literature are not statistically significant. Focusing on FX data (EBS limit order book) with 0.1s time resolution, we find that significance is impossible if the event log is incomplete (e. g. best quote changes). Transactions on the other hand can be tracked by analysing the respective volumes of transactions on both sides in each time slice. Assuming a constant exogenous activity rate and using parametric kernels , fits of trade activity satisfy Kolmogorov-Smirnov tests for about an hour , provided that the kernel consists of at least two exponentials; the endogeneity factor does not depend on the time of the day and is about 0.7. Significant fits of a full day can be achieved if one accounts for intra-day variability of exogenous activity, which yields a larger endogeneity factor ( 0.8 ). We could not obtain significant fits beyond a single day. Variable seasonalities are major obstacles to fitting FX activity with Hawkes processes accurately and result in larger apparent endogeneity factors and lower statistical significance .
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 .
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Focusing on FX data (EBS limit order book) with 0.1s time resolution, we find that significance is impossible if the event log is incomplete (e. g. best quote changes). Transactions on the other hand can be tracked by analysing the respective volumes of transactions on both sides in each time slice. Assuming a constant exogenous activity rate and using parametric kernels , fits of trade activity satisfy Kolmogorov-Smirnov tests for about an hour , provided that the kernel consists of at least two exponentials; the endogeneity factor does not depend on the time of the day and is about 0.7. Significant fits of a full day can be achieved if one accounts for intra-day variability of exogenous activity, which yields a larger endogeneity factor (
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
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). We could not obtain significant fits beyond a single day. Variable seasonalities are major obstacles to fitting FX activity with Hawkes processes accurately and result in larger apparent endogeneity factors and lower statistical significance