We develop Hawkes models in which events are triggered through self as well as cross-excitation. We examine whether incorporating cross-excitation improves the forecasts of extremes in asset returns compared to only self-excitation. The models are applied to US stocks, bonds and dollar exchange...

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...

A key application of long memory time series models concerns inflation. Long memory implies that shocks have a long-lasting effect. It may however be that empirical evidence for long memory is caused by neglecting one or more level shifts. Since such level shifts are not unlikely for inflation,...