Is there a goodness-of-fit chi-square test for muli-factor SDE models?

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I read in the book 'Modeling with Itô Stochastic Differential Equations' by Edward Allen about a chi-square test for SDE models. In section 5.5 this test is explained for a one-factor model.

Can this test be generalized for multi-factor models? Can such a test be used for the Chen model (short rate model) for instance?

I need a test for such a model, I've looked for one by searching on the Internet. Unfortunately I didn't find any. However, I do know that there are other kinds of chi-square tests that may be used if the model was calibrated by using the Efficient Method of Moments (for instance).