Evaluating exponential GARCH models

In this paper, a unified framework for testing the adequancy of an estimated EGARCH model is presented. The tests are Lagrange multiplier or Lagrange multiplier type tests and include testing an EGARCH model against a higher-order one and testing parameter constancy. Furthermore, various existing ways of testing the EGARCH model against GARCH one are investigated as another check of model adequacy. This is done by size and power simulations. Small-sample properties of the other tests are also investigated by simulations.