A double diffusion model

Mota, P., and M. L. Esquível. "A double diffusion model." (Submitted).


In earlier studies we have defined regime switching diffusion processes by considering one or two thresholds and regime switching occurring by a change in the diffusion drift and/or volatility functions parameters of a stochastic differential equation whose solution defines a continuous time diffusion process. The change in regime occurs whenever the trajectory of the process crosses a threshold, eventually with some delay. In this paper we generalize those results by allowing the underlying diffusion process to change from one family of diffusions in one regime to an entirely different one in the other regime. We propose an estimation procedure for all the parameters, namely the thresholds, the delay and for both regimes diffusion's parameters.