The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps
用MA(1)-GARCH(1,1)-跳跃过程模型分析1979-1991年欧洲货币体系各国货币对德国马克的周汇率，发现均值回归、波动率变化和跳跃行为，并用拟合优度检验比较了伯努利与泊松跳跃过程。
Weekly rates of the European Monetary System (EMS) vis-à-vis the Deutsche mark from April 1979 to March 1991 are modeled as a combined MA (1)–GARCH(1, 1)–jump process. The moving average (MA) part accounts for mean reversion required for the rates to stay inside the target zone. The generalized autoregressive conditional heteroscedasticity (GARCH) part accounts for changing volatility, whereas the jump process models parity changes and other erratic movements. Using an adjusted Pearson chi-squared goodness-of-fit test, we find similar results for the Bernoulli and the Poisson jump processes. In those cases in which the Bernoulli–normal distribution does not pass the goodness-of-fit test, a mixture of three normals does. Finally the MA(1)–GARCH(1, 1)–Bernoulli jump models are jointly estimated assuming a constant contemporaneous correlation matrix for the disturbances and a common jump probability for all the currencies.