This paper investigates the statistical relationship of the GARCH model and its di usion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's de ciency distance. To our surprise, we are able to show that the GARCH model and its di usion limit are asymptotically equivale...

The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all parameters at once. We demonstrate that how the HMC reproduces the GARCH parameters correctly. The algorithm is rather general and it can be applied to other ...

A distinguishing feature of the intra-day time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type due mainly to time-of-the-day phenomena. In this work we introduce a model able to describe the empirical evidence given by this periodic longmemory behaviour. The model, named PLM-GARCH (Periodic Long Memory GARCH), represents a natural e...

We present a new procedure for detecting multiple additive outliers in GARCH(1,1) models at unknown dates. The outlier candidates are the observations with the largest standardized residual. First, a likelihood-ratio based test determines the presence and timing of an outlier. Next, a second test determines the type of additive outlier (volatility or level). The tests are shown to be similar wi...

We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(1,1) model is seen to perform best.

Time varying correlations are often estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation models is proposed. These have the  exibility of univariate GARCH models coupled with parsimonious parametric models for the c...