A Two-stage Estimation Approach of Continuous-time Series Models with Jumps

Abstract

In modern financial economics continuous time-series diffusion models are more convenient to deal with than discrete time models when they are used to depict important economic variables such as stock prices, exchange rates and interest rates. A two-stage estimation approach is proposed to deal with the continuous-time models with jumps, in which the initial settings are quite resilient. This paper presents an example: first, the realized volatility theory is applied to the jumps and diffusion parameters of the model; then it uses forward Kolmogorov equation of actual price distribution at steady state to estimate the drift parameters. The model relies little on initial settings and optimization algorithms. The empirical results show that the estimations are stable and reliable. Hence the model is easier to extend to the estimation of complex set continuous time series.