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...

We study the development of conjunctive keyword searchable scheme which enables one to search encrypted documents by using more than one keyword. The notion of conjunctive keyword searching was presented by Golle et al. in 2004. However, their security model was constructed in a symmetric-key setting which is not applicable for the overall applications in the reality. So Park et al. extended Go...

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter...

We collect some continuous time GARCH models and report on how they approximate discrete time GARCH processes. Similarly, certain continuous time volatility models are viewed as approximations to discrete time volatility models. 1 Stochastic volatility models and discrete GARCH Both stochastic volatility models and GARCH processes are popular models for the description of financial time series....

This paper examines the behaviour of European option price (Duan (1995)) and the Black-Scholes model bias when stock returns follow a GARCH (1,1) process. The GARCH option price is not preferenceneutral and depends on the unit risk premium (λ) as well as the two GARCH (1,1) process parameters (α1 , β1). In general, the GARCH option price does not seem overly sensitive to these parameters. Deep-...

The predictability of network traffic is a significant interest in many domains such as congestion control, admission control, and network management. An accurate traffic prediction model should have the ability to capture prominent traffic characteristics, such as long-range dependence (LRD) and self-similarity in the large time scale, multifractal in small time scale. In this paper we propose...

The predictability of network traffic is a significant interest in many domains such as congestion control, admission control, and network management. An accurate traffic prediction model should have the ability to capture prominent traffic characteristics, such as long-range dependence (LRD) and self-similarity in the large time scale, multifractal in small time scale. In this paper we propose...

Although the GARCH model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and lepto...

We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-taile...