We develop univariate regime-switching GARCH (RS-GARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specified as a function of past information. We provide sufficient conditions for geometric ergodicity and existence of moments. Because of path dependence, maximum likelihood estimation is no...

This paper presents a method for computing the explicitly rational solutions of a trivariate rational system of autonomous ordinary differential equations (ODEs) based on the proper parametrization of its invariant algebraic space curve. It is the generalization of the method in [11]. First, an undetermined coefficients method is given for computing the invariant algebraic space curves of the t...

Factor models are well established as promising alternatives to obtain covariance matrices of portfolios containing a very large number of assets. In this paper, we consider a novel multivariate factor GARCH specification with a flexible modeling strategy for the common factors, for the individual assets, and for the factor loads. We apply the proposed model to obtain minimum variance portfolio...

This paper presents a GARCH type volatility model with a time-varying unconditional volatility which is a function of macroeconomic information. It is an extension of the SPLINE GARCH model proposed by Engle and Rangel (2005). The advantage of the model proposed in this paper is that the macroeconomic information available (and/or forecasts) is used in the parameter estimation process. Based on...

In this paper, we propose a bounded influence estimation (BIE) and outlier detection procedure for GARCH models. Previous studies show that maximum likelihood estimates of GARCH models are sensitive to outliers and financial time series present a heavy tail due to outliers. The proposed BIE limits the influence of a small subset of the data and is asymptotically normal. Its robustness against o...

Methods: One commodity future from each group of futures is chosen for the analysis. The select commodities are potato, gold, crude oil, and mentha oil. The data are collected from MCX India over the period 2004–2012. This study uses several econometric techniques for the analysis. The GARCH model is introduced for examining the volatility of commodity futures. One of the key contributions of t...

The generalized autoregressive conditional heteroscedasticity (GARCH) approach is one of the common and simpler ways to use historical data to produce estimates of current and future levels of volatilities. This model recognizes that volatilities are not constant, for instance, a particular volatility may be high or low depending on the period of time. One of goals of a GARCH model is to track ...

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and βmixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estim...

Several aspects of GARCH(p, q) models that are relevant for empirical applications are investigated. In particular, it is noted that the inclusion of dummy variables as regressors can lead to multimodality in the GARCH likelihood. This invalidates standard inference on the estimated coefficients. Next, the implementation of different restrictions on the GARCH parameter space is considered. A re...

This paper develops a new econometric framework for investigating how the sensitivity of the financial market volatility to shocks varies with the volatility level. For this purpose, the paper first introduces the square-root (SQ) GARCH model for financial time series. It is an ARCH analogue of the continuous-time square-root stochastic volatility model popularly used in derivatives pricing and...