This paper develops the approximate bias of the ordinary least squares estimator of the mean reversion parameter in continuous-time Lévy processes. Several cases are considered, depending on whether the long-run mean is known or unknown and whether the initial condition is fixed or random. The...

We derive the exact distribution of the maximum likelihood estimator of the mean reversion parameter (k) in the Ornstein-Uhlenbeck process by employing numerical integration via analytical evaluation of a joint characteristic function. Different scenarios are considered: known or unknown drift...

Eric Ghysels is the Bernstein Distinguished Professor of Economics and Professor of Finance at University of North Carolina at Chapel Hill. In 2008, Eric Ghysels and Robert Engle (2003 Nobel co-Laureate in Economic Science with Clive Granger) founded the Society for Financial Econometrics...

A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date-stamping the origination and collapse of economic exuberance, and providing valid con?dence intervals for explosive growth rates. The method involves the recursive im- plementation of a...

This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is...

Econometric analysis of continuous time models has drawn the attention of Peter Phillips for nearly 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and econometric problems, from univariate equations to...

In this paper we develop and implement a method for maximum simulated likelihood estimation of the continuous time stochastic volatility model with the constant elasticity of volatility. The approach do not require observations on option prices nor volatility. To integrate out latent volatility...

It is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in finite discrete samples and in large in-fill samples. In this paper, we obtain two expressions to approximate the bias of the least...