Title: Efficiently estimating discrete and continuous time GARCH models with irregularly spaced observations
Authors: William Dunsmuir - The University of New South Wales (Australia) [presenting]
Abstract: There are essentially two continuous time limits of GARCH(1,1) processes as the time between observations shrinks to zero. The first, the bivariate diffusion limiting process does not allow jumps in the continuous time limit process. The COGARCH process defined in terms of a Levy process can also be obtained as the continuous time limit of the discrete time GARCH(1,1) process. The COGARCH process has a single source of driving noise and allows jumps. Because the number, time location and size of jumps cannot be observed directly using equally or irregularly spaced observations on the continuous time process the likelihood for the COGARCH model is intractable and requires careful computational implementation. Sequential Monte Carlo (SMC) with a continuous resampling method to estimate the likelihood function and ensure it is continuous in the parameters is used. We show that the SMC based method outperforms the quasi-maximum likelihood methods previously proposed in the literature in terms of bias and standard errors of estimation. Application to high frequency financial returns data will be presented. The SMC approach can also be used to estimate the parameters of traditional discrete time GARCH models and variants such as the Markov regime switching GARCH model when they are irregularly observed. Illustrations for financial time series as well as high frequency wind measurements will also be presented.