Estimation and Testing in Models Containing Both Jumps and Conditional Heteroscedasticity

Abstract

In this article we develop a test for the hypothesis that a series (observed in discrete time) is generated by a diffusion process. This test is based on an overidentifying relation between variance and kurtosis parameters that holds for generalized autoregressive conditional heteroscedastic diffusions. The proposed test is not specific to a particular data frequency and clearly indicates the presence of jumps in dollar exchange rates. To assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroscedasticity.

KEY WORDS:

• Continuous-time GARCH
• Exchange rates
• Jump diffusion
• Weak GARCH