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...

We reveal that in the estimation of univariate GARCH or multivariate generalized orthogonal GARCH (GO-GARCH) models, maximizing the likelihood is equivalent to making the standardized residuals as independent as possible. Based on that, we propose three factor GARCH models in the framework of GO-GARCH: independent-factor GARCH exploits factors that are statistically as independent as possible; ...

We test the importance of multivariate information for modelling and forecasting inflation’s conditional mean and variance. In the literature, the existence of inflation’s conditional heteroskedasticity has been debated for years, as it seemed to appear only in some datasets and for some lag lengths. This phenomenon might be due to the fact that inflation depends on a linear combination of econ...

In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persisten...

How persistent is volatility? In other words, how quickly do financial markets forget large volatility shocks? Figure 1.1, Shephard (attached) shows that daily squared returns on exchange rates and stock indices can have autocorrelations which are significant for many lags. In any stationary ARCH or GARCH model, memory decays exponentially fast. For example, if {εt } are ARCH (1), the {εt} have...

This paper focuses on the performance of various GARCH models in terms of their ability of delivering volatility forecasts for stock return data. Volatility forecasts obtained from a variety of mean and variance specifications in GARCH models are compared to a proxy of actual volatility calculated using daily data. In-sample tests suggest that a regression of volatility estimates on actual vola...

This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our re...