Recently, there has been a growing interest in the methods addressing volatility in computational finance and econometrics. Peiris et al. [8] have introduced doubly stochastic volatility models with GARCH innovations. Random coefficient autoregressive sequences are special case of doubly stochastic time series. In this paper, we consider some doubly stochastic stationary time series with GARCH ...

We use high-frequency intra-day realized volatility to evaluate the relative forecasting performance of several models for the volatility of crude oil daily spot returns. Our objective is to evaluate the predictive ability of time-invariant and Markov switching GARCH models over different horizons. Using Carasco, Hu and Ploberger (2014) test for regime switching in the mean and variance of the ...

The research of Kim and Schmidt (1993) is extended to examine the properties of asymmetric unit root tests in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). Using Monte Carlo simulation, threshold autoregressive and momentum—threshold autoregressive asymmetric unit tests are shown to suffer greater size distortion than the original (implicitly symmetric) Dick...

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the standard deviat...

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we...

Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of returns. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estim...

The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstr...

We consider the estimation of a random level shift model for which the series of interest is the sum of a short memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1−α) and is a random variable with probability α. Our estimation...

Conditional quantile estimation is an essential ingredient in modern risk management. Although GARCH processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this paper, we study esti...

This paper characterizes the term structure of risk measures such as Value at Risk (VaR) and expected shortfall under different econometric approaches including multivariate regime switching, GARCH-in-mean models with student-t errors, two-component GARCH models and a non-parametric bootstrap. We show how to derive the risk measures for each of these models and document large variations in term...