Estimation of Dynamic Mixed Hitting Time Model Using Characteristic Function Based Moments

Abstract

We present a characteristic function-based method for the estimation of dynamic mixed hitting time model for duration between events and price changes. The model specifies duration between events as the first time a latent component of multivariate Brownian motion crosses a random boundary. Meanwhile, another (correlated) Brownian component generates the prices. The proposed estimation method facilitates computation and overcomes problems related to the discretization error in the moment conditions and the non-tractability in the joint probability density function. An empirical application using transaction level data on stocks of a large capitalization company traded on the Indonesia Stock Exchange is illustrated. Estimation results suggest that durations and return volatility have strong persistence and, further, there is a negative instantaneous relation between volatility and contemporaneous duration. The impact of considering the causality relation between volatilities and durations on instantaneous volatility estimate are also investigated.