Specification Testing in Hawkes Models

Tinbergen Institute Discussion Paper 15-086/III

38 Pages Posted: 25 Jul 2015 Last revised: 9 Sep 2015

See all articles by Francine Gresnigt

Francine Gresnigt

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE)

Erik Kole

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute; ERIM; Tinbergen Institute

Philip Hans Franses

Erasmus University Rotterdam (EUR) - Department of Econometrics

Date Written: July 24, 2015

Abstract

We propose various specification tests for Hawkes models based on the Lagrange Multiplier (LM) principle. Hawkes models can be used to model the occurrence of extreme events in financial markets. Our specific testing focus is on extending a univariate model to a multivariate model, that is, we examine whether there is a conditional dependence between extreme events in markets. Simulations show that the test has good size and power, in particular for sample sizes that are typically encountered in practice. Applying the specification test for dependence to US stocks, bonds and exchange rate data, we find strong evidence for cross-excitation within segments as well as between segments. Therefore, we recommend that univariate Hawkes models be extended to account for the cross-triggering phenomenon.

Keywords: Hawkes processes, specification tests, extremal dependence, financial crashes

JEL Classification: C12, C22, C32, C52

Suggested Citation

Gresnigt, Francine and Kole, Erik and Franses, Philip Hans, Specification Testing in Hawkes Models (July 24, 2015). Tinbergen Institute Discussion Paper 15-086/III, Available at SSRN: https://ssrn.com/abstract=2635436 or http://dx.doi.org/10.2139/ssrn.2635436

Francine Gresnigt (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

Erik Kole

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 12 58 (Phone)

HOME PAGE: http://people.few.eur.nl/kole

ERIM

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

HOME PAGE: http://people.few.eur.nl/kole

Philip Hans Franses

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1278 (Phone)
+31 10 408 9162 (Fax)

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