|タイトル||Topics in continuous time limits of discrete time GARCH models and estimation of the COGARCH model|
|開催日時||2016年3月2日 16:00-17:00 ※コーヒータイム、懇親会はなし|
|講演者||William Dunsmuir 氏（ニューサウスウェールズ大学）|
|内容||There are essentially two continuous time limits of the GARCH(1,1) model as the time between observations shrinks to zero: the classical Nelson double diffusion limit and the more recent COGARCH process defined in terms of a Levy process. Both of these can be obtained as special cases of a general setup which we call continuous delay GARCH (CDGARCH for short) in which the orders p and q of the GARCH(p;q) process can diverge to innity as the time between observations shrinks to zero.
The first part of the talk will explain these general results and illustrate the extension from GARCH(1,1) limits to the CDGARCH framework. The second part of the talk will discuss the estimation of the COGARCH model for unequally spaced observation times.
The likelihood for the COGARCH model is intractable and requires careful computational implementation.
In particular the use of sequential Monte Carlo is used to estimate the likelihood function and the estimates obtained are superior to the quasi-maximum likelihood methods previously proposed in the literature.
Application to high frequency nancial returns data will by presented.
(The First part of the talk is joint work with Cuong Tran and Ben Goldys. The secondpart of the talk is joint work with Damien Wee and Feng Chen)