We propose a novel, simple, effi cient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box-Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.

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It is shown that a class of tailed shift chaotic maps can be designed with substantial negative dependence, both linear and non-linear, and that extended Perron±Frobenius theory gives their dependence structure. Using a simpli®ed chaos-based communication system, it is shown that chaotic spreading sequences with low kurtosis and negative non-linear mean-centred quadratic autocorrelations can improve bit-received accuracy. This quadratic form of non-linear dependence is investigated and shown to be statistically sensible.

A ®rst-order autoregressive process with one-dimensional inverse Gaussian marginals is introduced. The innovation distributions are obtained in certain special cases. The unknown parameters are estimated using different methods and these estimators are shown to be consistent and asymptotically normal. Performance of the estimators is discussed using simulation experiments.

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This paper presents gamma stochastic volatility models and investigates its distributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The in-sample analysis shows that return models with gamma autoregressive stochastic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out-of-sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance compared to GARCH and EGARCH models. Copyright © 2006 John Wiley _ Sons, Ltd.

a b s t r a c tWhen variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type. . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution.