ARCH processes and their extensions known as GARCH processes are widely accepted for modelling financial time series, in particular stochastic volatility processes. The offline estimation of ARCH and GARCH processes have been analyzed under a variety of conditions in the literature. The main contribution of this paper is a rigorous convergence analysis of a recursive estimation method for GARCH...

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...

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ARCH/GARCH modelling has been successfully applied in empirical finance for many years. This paper surveys the semiparametric and nonparametric methods in univariate andmultivariate ARCH/GARCHmodels. First, we introduce some specific semiparametric models and investigate the semiparametric and nonparametrics estimation techniques applied to: the error density, the functional form of the volatil...

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 an alytically that both the asymptotic size and power are adversely a ected if AO s are neglected the test rejects the null hypothesis of homoskedasticity too often when it is in fact tr...

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...

A new variant of the ARCH class of models for forecasting conditional variance, to be called the Generalized AutoRegressive Conditional Heteroskedasticity Parkinson Range (GARCH-PARK-R) Model, is proposed. The GARCH-PARK-R model, utilizing the extreme values, is a good alternative to the Realized Volatility that requires a large amount of intra-daily data, which remain relatively costly and are...

This paper applies six recently developed nonparametric tests of serial independence to monthly US stock returns. Findings of previous studies based on the BDS test are supported since most of the new tests also reject the random walk hypothesis. Furthermore, power properties of the new tests are compared with those of the BDS test. The latter has much power against ARCH and GARCH alternatives ...

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented GARCH(1,1) sequences and the asymptotic distribution of various ...