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-...

We are interested in estimation of stationary GARCH models. In simulation studies, we assess the performance of the maximum likelihood estimator and Yule-Walker estimator of the GARCH (1, 1) model. Finally we attempt to fit the dynamics of daily stock returns on Nordea by a GARCH model.

Most existing econometric models such as ARCH(q) and GARCH(p,q) take into account heteroskedasticity (non-stationarity) of time series. However, the original ARCH(q) and GARCH(p,q) models do not take into account the asymmetry of the market’s response to positive and to negative changes. Several heuristic modifications of ARCH(q) and GARCH(p,q) models have been proposed that take this asymmetry...

The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The model can be regarded as a generalization to a multivariate setting of the univariate BLGARCH model proposed by Storti and Vitale (2003a; 2003b). It is shown how MBL-GARCH models allow to account for asymmetric effects in both conditional variances and correlations. An EM...

Traditional GARCH models describe volatility levels that evolve smoothly over time, generated by a single GARCH regime. However, nonstationary time series data may exhibit abrupt changes in volatility, suggesting changes in the underlying GARCH regimes. Further, the number and times of regime changes are not always obvious. This article outlines a nonparametric mixture of GARCH models that is a...

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 ...

Financial time series exhibit time-varying volatilities and non-Gaussian distributions. There has been considerable research on the GARCH models for dealing with these issues related to financial data. Since in practice the true error distribution is unknown, various quasi maximum likelihood methods based on different assumptions on the error distribution have been studied in the literature. Ho...