Specification test for segmented time-varying diffusion models

Abstract

In this paper, a generalized residual goodness of fit test is proposed as an improvement on an existing test method for one-dimension diffusion models. By comparative analysis, we find that the generalized residual goodness of fit test is an effective test method. When diffusion models are used to describe stock prices, interest rates and exchange rates, the parameters of their drift function and diffusion function will change over time rather than be constants due to changeful economic environment. Based on this idea, we propose a diffusion model with segmented time-varying parameters. The test proposed above is used to examine the segmented time-varying characteristic of the model parameters.