Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. This new class of periodic autoregressive conditional heteroscedasticity, or P-ARCH, models is directly related to the class o...

We address the IGARCH puzzle, by which we understand the fact that a GARCH(1,1) model fitted to virtually any financial dataset exhibit the property thatˆα + ˆ β is close to one. We do this by proving that if data is generated by a stochastic volatility model but fitted to a GARCH(1,1) model one would get thatˆα + ˆ β tends to one in probability as the sampling frequency is increased. We also d...

In recent decades, the momentum of global environmental protection has culminated in the Kyoto Agreement of 1998, placing the limelight on “green” issues. This paper argues that the protection of environmental systems involves a fragile balance between the costs of environment preservation and the profit motivations of industrialists. In particular, one of the issues that needs to be addressed ...

In this paper we investigate the properties of the Lagrange Multiplier (LM) test for autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AO's). We show analytically that both the asymptotic size and power are adversely aaected if AO's are neglected: the test rejects the null hypothesis of homoskedasticity too often when it is i...

We propose a model that extends the RT-GARCH by allowing conditional heteroskedasticity in volatility process. show we are able to filter and forecast both of simultaneously this simple setting. The function follows second-order difference equation as opposed first-order under GARCH(1,1) RT-GARCH(1,1). Empirical studies confirm presence process standardised residuals return close Gaussian model...

In this paper the value at risk (VaR) forecasts are compared using three different GARCH models; ARCH(1), GARCH(1,1) and EGARCH(1,1). The implemented method is a one-day ahead out of sample forecast of the VaR. The forecasts are evaluated using the Kupiec test with a five percent significance level. The focus is on three different markets; commodities, equities and exchange rates. The goal of t...

Detecting and modelling structural changes in GARCH processes have attracted a great amount of attention in time series econometrics over the past few years. In this paper, we …rst generalize Dahlhaus and Subba Rao (2006 2008)’s time-varying ARCH processes to time-varying GARCH processes and derive the consistency and asymptotic normality of the weighted quasi maximum likelihood estimator of th...

This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two diierent regimes with a smooth transition function. In one formulation, the conditional variance reacts diierently to negative and positive shocks while in a second formulation, small and big shocks have separate eeects. The introduction of a threshold allows for a mixed eeect. A Bayesian strategy, based...

We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows conditional variance log-returns each bank to depend on past volatility shocks other and their squared in parsimonious way. backtesting resulting measures provides evidence that (i) multivariate GARCH...

GARCH model has gained popularity during the last two decades, because of their ability to capture non-linear dynamics in the real life data which we often observe especially in financial markets. This paper discuss four common information criteria (AIC, AICc, BIC and HQ) and their ability of correct selection in the presence of GARCH effect, based on their probability of correct selection as a...