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...

In this article we present a new model of the spot interest rate and a new method of estimation of nonlinear stochastic differential equations. We show how an integrated discrete time process in an econometric sense can be modelled by a continuous time ergodic process. We make an application to...

In this work we motivate the use of second-order stochastic differential equations in economics and finance. We provide an empirical illustration and discuss a parametric second-order stochastic differential equation for stock prices and exchange rates.

This article presents a new simulation-based technique for estimating the likelihood of stochastic differential equations. This technique is based on a result of Dacunha-Castelle and Florens-Zmirou. These authors proved that the transition densities of a nonlinear diffusion process with a...

From the discrete-time Exponential Smooth Autoregressive model, we obtain a continuous-time version that provides new tools for analyzing the Purchasing Power Parity hypothesis.

This paper proposes a new concept: the usage of Multivariate Markov Chains (MMC) as covariates. Our approach is based on the observation that we can treat possible categorical (or discrete) regressors, whose values are unknown in the forecast period, as an MMC in order to improve the forecast...