Specification Testing in Hawkes Models
Tinbergen Institute Discussion Paper 15-086/III
38 Pages Posted: 25 Jul 2015 Last revised: 9 Sep 2015
Date Written: July 24, 2015
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: Suggested Citation