STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

Liudas Giraitis · Piotr S. Kokoszka · Remigijus Leipus

253 citations0/0 files storedEconometric Theory

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Financial Risk and Volatility Modeling Complex Systems and Time Series Analysis Time Series Analysis and Forecasting

Abstract

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

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References

1994Modelling of extremal events in insurance and finance 1996Fractionally integrated generalized autoregressive conditional heteroskedasticity 1996Long memory processes and fractional integration in econometrics 1990Stationarity and Persistence in the GARCH(1,1) Model 1996Modeling volatility persistence of speculative returns: A new approach 1998The detection and estimation of long memory in stochastic volatility 1992Inequality Constraints in the Univariate GARCH Model 1993A geographical model for the daily and weekly seasonal volatility in the foreign exchange market

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2006Statistical inference for time-varying ARCH processes 2009An Introduction to Univariate GARCH Models 2006Inequality Constraints in the Fractionally Integrated GARCH Model 2007Robust estimates for GARCH models 2002Microeconomic Models for Long Memory in the Volatility of Financial Time Series 2005Volatility Forecasting

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