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Multivariate Hawkes processes: an application to financial data. (English) Zbl 1242.62093
A Hawkes process is also known under the name of a self-exciting point process and has numerous applications. The authors introduce the multivariate Hawkes process with points \((t_i,d_i,x_i)\), where \(t_i\) is the time, \(d_i\in\{1,\dots,d\}\) indicates the component and \(x_i\) is a real-valued mark, and the Hawkes process with vector-valued marks \(x_{i1},\dots,x_{id}\) whose points are \((t_i,x_{i1},\dots,x_{id})\). The authors recall the conditions for the existence and then work out the maximum likelihood approach for the parameter estimation and graphical tools for the goodness-of-fit for multivariate Hawkes processes with possibly dependent marks. As an application, the authors analyse two financial data sets.

MSC:
62M09 Non-Markovian processes: estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M30 Inference from spatial processes
91G70 Statistical methods; risk measures
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