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...

We consider the parameter restrictions that need to be imposed in order to ensure that the conditional variance process of a GARCH(p, q) model remains non-negative. Previously, Nelson and Cao (1992) provided a set of necessary and sufficient conditions for the aforementioned non-negativity property for GARCH(p, q) models with p ≤ 2, and derived a sufficient condition for the general case of GAR...

We revisit the risk-return relation using the component GARCH model and international daily MSCI stock market data. In contrast with the previous evidence obtained from weekly and monthly data, daily data show that the relation is positive in almost all markets and often statistically significant. Likelihood ratio tests reject the standard GARCH model in favor of the component GARCH model, whic...

It is well known in the literature that the joint parameter estimation of the Smooth Autoregressive – Generalized Autoregressive Conditional Heteroskedasticity (STAR-GARCH) models poses many numerical challenges with unknown causes. This paper aims to uncover the root of the numerical difficulties in obtaining stable parameter estimates for a class of three-regime STAR-GARCH models using Quasi-...

The univariate Generalised Autoregressive Conditional Heterscedasticity (GARCH) model has successfully captured the symmetric conditional volatility in a wide range of time series financial returns. Although multivariate effects across assets can be captured through modelling the conditional correlations, the univariate GARCH model has two important restrictions in that it: (1) does not accommo...

In this paper we consider a general ...rst-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for ...rstorder exponential and logarithmic GARCH processes. These autocorrelations decay exponentially with the lag and may be used for checkin...

This paper proposes a new parametric volatility model that introduces serially dependent innovations in GARCH specifications. We first prove the asymptotic normality of the QML estimator in this setting, allowing for possible explosive and nonstationary behavior of the GARCH process. We show that this model can generate an alternative measure of risk premium relative to the GARCH-M. Finally, we...