Financial Time Series Models and Applications

Abstract

Duration models are often concerned with time intervals between trades, longer durations indicating a lack of trading activities. In this thesis, we study parameter estimation for the Autoregressive Conditional Duration (ACD) and Stochastic Conditional Duration (SCD) models. Maximum likelihood methods can usually be used in the case of ACD models. However, the SCD models are based on the assumption that durations are generated by a dynamic stochastic latent variable which is often perturbed by Exponential, Weibull, Gamma or Log-Normal distributed innovations. This makes the use of maximum likelihood methods difficult.

One alternative method of parameter estimation, in this case, consists in using quasi-maximum likelihood after transforming the original nonlinear model into a state-space model and using the Kalman filter, a similar filtering scheme or the Generalized Method of Moments (GMM). We use the nonlinear filter and GMM method to analyze the Quadratic Stochastic Conditional duration model as well.