Estimation On SCD Model Based On Non-Gaussian State Space Model

State space model is used in a wide range of applications, because it can bring unobservable variables into observation equation and estimate them together to get result through the estimation of Kalman filter and smoother with powerful recursive algorithms. Many econometric models, such as ARMA model, GARCH family models and SV family models, can be estimated after being transformed into state space models. Early theory of state space models is based on the normal assumption of disturbances and initial state vector. But we are forced to develop non-Gaussian nonlinear state space models and study the more extensive extended Kalman filter and smoother which are applicable underneath, because our assumption is not reasonable on numerous economic variables. Under this background, this paper emphatically studies non-Gaussian state space model and transforms it into approximating linear state space model by using a first order Taylor expansion. Three forms that frequently appear in economic variables are considered with regard to non-Gaussian distribution in this paper and specific solutions are provided for the three refined models and extended Kalman filter and smoothing is deduced accordingly. Gaussian importance sampling based on Monte Carlo simulation is used in this paper. Our simulation techniques are on the basis of independent samples instead of Markov chains, which enables us to avoid convergence problems and also to obtain simple and accurate estimates of sampling variances due to simulation. Meanwhile, the analysis and modeling of high-frequency and ultrahigh-frequency time series has become a new research field of econometrics in recent years and Stochastic Conditional Duration model studying the arrival time of market events in financial markets is considered to be an excellent model. Although stochastic variables are introduced into the model to better fit the proper statistical characteristics of high-frequency and ultrahigh-frequency financial time series, they also bring troubles to this model.In view of the respective advantages of non-Gaussian state space model and SCD model, we transform SCD model into non-Gaussian state space model and consequently solve the estimation problems of SCD model by using extended Kalman filter. The empirical results prove the feasibility of our estimation method and show the following advantages: The calculation is more effective and the estimates are more precise.