Testing for jumps in conditionally Gaussian ARMA–GARCH models, a robust approach

Financial asset prices occasionally exhibit large changes. To deal with their occurrence, observed return series are assumed to consist of a conditionally Gaussian ARMA–GARCH type model contaminated by an additive jump component. In this framework, a new test for additive jumps is proposed. The test is based on standardized returns, where the first two conditional moments of the non-contaminated observations are estimated in a robust way. Simulation results indicate that the test has very good finite sample properties, i.e. correct size and high proportion of correct jump detection. The test is applied to daily returns and detects less than 1% of jumps for three exchange rates and between 1% and 3% of jumps for about 50 large capitalization stock returns from the NYSE. Once jumps have been filtered out, all series are found to be conditionally Gaussian. It is also found that simple GARCH-type models estimated using filtered returns deliver more accurate out-of sample forecasts of the conditional variance than GARCH and Generalized Autoregressive Score (GAS) models estimated from raw data.