This paper introduces a novel Ito diffusion process to model high-frequency financial data, which can accommodate low-frequency volatility dynamics by embedding the discrete-time non-linear exponential GARCH structure with log-integrated in continuous instantaneous process. The key feature of proposed is that, unlike existing GARCH-Ito models, has structure, ensures that volatilities have reali...

While ARCH/GARCH equations have been widely used to model financial market data, formal explanations for the sources of conditional volatility are scarce. This paper presents a model with the property that standard econometric tests detect ARCH/GARCH effects similar to those found in asset returns. We use evolutionary game theory to describe how agents endogenously switch among different foreca...

This note investigates impacts of multivariate generalised autoregressive conditional heteroskedasticity (GARCH) errors on hypothesis testing for cointegrating vectors. The study reviews a cointegrated vector autoregressive model incorporating multivariate GARCH innovations and a regularity condition required for valid asymptotic inferences. Monte Carlo experiments are then conducted on a test ...

In this paper we test for (Generalized) AutoRegressive Conditional Heteroskedasticity [(G)ARCH] in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier [LM] test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of 5 years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulat...

In this paper, we quantify market risk at an intraday time horizon using normal GARCH, Student GARCH, RiskMetrics and high-frequency duration (Log-ACD) models set in the framework of the conditional VaR methodology. Because of the small time horizon of the intraday returns (15 and 30 minute returns in this paper), an evaluation of intraday market risk can be useful to market participants (trade...

In this paper, we introduce supergaussian generalized autoregressive conditional heteroscedasticity (GARCH) models for speech signals in the short-time Fourier transform (STFT) domain. We address the problem of speech enhancement, and show that estimating the variances of the STFT expansion coefficients based on GARCH models yields higher speech quality than by using the decision-directed metho...

This paper provides a solution for the multiple changepoint detection problems in financial time series prediction without knowing the number and location of changepoints. The proposed approach is a Sequential Monte Carlo (SMC) method for estimating GARCH based volatility models which are subject to an unknown number of changepoints. Recent Auxiliary Particle Filtering (APF) techniques are used...

We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes. We show that the estimator of tail thickness is consistent and converges at rate √ T to a normal distribution (where T is...

This paper investigates the statistical relationship of the GARCH model and its di usion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's de ciency distance. To our surprise, we are able to show that the GARCH model and its di usion limit are asymptotically equivale...

Markov switching GARCH models have been developed in order to address the statistical regularity observed in financial time series such as strong persistence of conditional variance. However, Maximum Likelihood Estimation faces a implementation problem since the conditional variance depends on all the past history of state. This paper shows that this problem can be handled easily in Bayesian in...