A discrete and a continuous-time model based on a technical trading rule

In this article we propose a model in discrete and continuous time that incorporates explicitly a technical trading rule in the specification of the volatility. The proposed discrete-time model is an alternative to GARCH-type processes. We derive conditions for the covariance and strict stationarity of the discrete-time process and we study the estimation and inference problems. We also analyze the conditions under which the discrete-time process converges in distribution to a diffusion process. To illustrate the proposed model and compare it with the GARCH specification, we analyze the daily closing stock prices of two major U.S. companies (Microsoft and Oracle), two stock indices (DAX and NASDAQ) and two U.S. Dollar exchange rates (Euro and Sterling) Copyright , Oxford University Press.