We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long-range correlations in the variance. We study the AR+GARCH process ...

We propose an autoregressive conditional duration (ACD) model with periodic time-varying parameters and multiplicative error form. name this (PACD). First, we study the stability properties moment structures of it. Second, estimate parameters, using (profile two-stage) Gamma quasi-maximum likelihood estimates (QMLEs), asymptotic which are examined under general regularity conditions. Our estima...

The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score. Keywords: Duration models; g...

The European Union carbon market is undergoing rapid development and its interdependence with fossil fuel markets is increasingly important for energy investors. In this study, exponential general autoregressive conditional heteroskedastic models, extreme value theory and copulas are used to evaluate downside risk through the traditional value-at-risk and expected shortfall measurements. Empiri...

Recent studies have suggested that stock markets' volatility has a type of long-range dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, diierent models for describing this long-range dependence are examined and the properties of a Long-Memory Stochastic Volatility (LMSV...

Abstract: This paper studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) and of a suggested modified version for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. The modified QMLE (MQMLE) is based on truncation of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (200...

This paper develops the method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. In order to provide a general framework being able to accommodate skewness, leptokurtosis, fat tails as well as the time varying volatility that are often found in financial data, generalized hyperbolic (GH) distribution is used for innovations. As t...