Modelling Financial High Frequency Data Using Point Processes

Abstract

In this paper, we give an overview of the state-of-the-art in the econometric literature on the modeling of so-called financial point processes. The latter are associated with the random arrival of specific financial trading events, such as transactions, quote updates, limit orders or price changes observable based on financial high-frequency data. After discussing fundamental statistical concepts of point process theory, we review durationbased and intensity-based models of financial point processes. Whereas duration-based approaches are mostly preferable for univariate time series, intensity-based models provide powerful frameworks to model multivariate point processes in continuous time. We illustrate the most important properties of the individual models and discuss major empirical applications.

Modelling interregional links in electricity price spikes

“…This approach draws on the econometrics of point processes, which have become popular in the financial econometrics literature (see Bauwens and Hautsch (2009) for a relatively recent survey). An early adaptation of duration models (Engle and Russell, 1997) dealing with both the occurrence of the event and the size of the event (marks), is the Autoregressive Conditional Hazard (ACH) model developed by Hamilton and Jordà (2002), who considered predicting changes in the United States Federal funds target rate.…”

The Hawkes process with renewal immigration & its estimation with an EM algorithm

“…Over the past decade, the Hawkes model has become very popular in financial applications, mostly for modeling highfrequency fluctuations of prices and limit order book dynamics (Bowsher, 2007;Bauwens and Hautsch, 2009;Toke, 2011;Cont, 2011;Aït-Sahalia et al, 2011;Filimonov and Sornette, 2012;Bacry et al, 2012;Chavez-Demoulin and McGill, 2012;Hardiman et al, 2013), and for the modeling of sequences of lower-frequency extreme events (Chavez-Demoulin et al, 2005;Errais et al, 2010;Embrechts et al, 2011). In this section, we present a data-driven motivating example for applications of the RHawkes model within the context of quantitative finance.…”

“…The exponential offspring density (32), which is typical for financial and econometric applications (Bowsher, 2007;Bauwens and Hautsch, 2009;Filimonov and Sornette, 2012;Embrechts et al, 2011;Aït-Sahalia et al, 2011), endows Markov properties to the model (Oakes, 1975), and is more robust to outliers than heavy-tailed alternatives (Filimonov and Sornette, 2015). A heavy-tailed offspring density (33) is typical for seismological applications (Ogata, 2013), where it accounts for the power law decay of aftershock activity with time (Omori's law).…”

“…In financial and econometrical applications, the Hawkes process is becoming the gold standard for modeling high frequency fluctuations of financial prices (see for instance Bowsher, 2007, Bauwens and Hautsch, 2009, Filimonov and Sornette, 2012, Bacry et al, 2012. Other recent applications include: modeling genomic events along DNA (Reynaud-Bouret and Schbath, 2010;Gusto and Schbath, 2005); neural spike trains (Krumin et al, 2010); brain seizures (Sornette and Osorio, 2010); and the spread of violence (Lewis et al, 2012) and crime (Lewis and Mohler, 2011a).…”

Analysis of ultra-high-frequency financial data using advanced Fourier transforms

“…Although the literature has suggested several econometric models to deal with this specific data type, such as (a) the ACD model (Engle and Russell, 1998) and its recent enhancements (for a comprehensive overview see Bauwens et al, 2004;Fernandes and Grammig, 2006;Bauwens and Hautsch, 2008), (b) count models or (c) intensity models (see Hall and Hautsch, 2006;Bauwens and Hautsch, 2006), none of these approaches seems apt to analyse the data both in realtime and within a multivariate framework. Duration models, as pointed out by Hall and Hautsch (2006), cannot consider more than a single process because of the asynchronisation problem of multivariate point processes (otherwise truncation is required as shown in Engle and Lunde, 2003).…”