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.

Additional Metadata
Keywords Hawkes processes, specification tests, extremal dependence, financial crashes
JEL Hypothesis Testing (jel C12), Time-Series Models; Dynamic Quantile Regressions (jel C22), Time-Series Models; Dynamic Quantile Regressions (jel C32), Model Evaluation and Testing (jel C52)
Publisher Tinbergen Institute
Persistent URL hdl.handle.net/1765/78462
Series Tinbergen Institute Discussion Paper Series
Citation
Gresnigt, F, Kole, H.J.W.G, & Franses, Ph.H.B.F. (2015). Specification Testing in Hawkes Models (No. TI 15-086/III). Tinbergen Institute Discussion Paper Series. Tinbergen Institute. Retrieved from http://hdl.handle.net/1765/78462