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Gouriéroux and Zakoïan (2013) propose to use noncausal models to parsimoniously capture nonlinear features often observed in financial time series and in particular bubble phenomena. In order to distinguish causal autoregressive processes from purely noncausal or mixed causal-noncausal ones, one has to depart from the Gaussianity assumption on the error distribution. Financial (and to a large extent macroeconomic) data are characterized by large and sudden changes that cannot be capturedby the Normal distribution, which explains why leptokurtic error distributions are often considered in empirical finance. By means of Monte Carlo simulations, this paper investigates the identication of mixed causal-noncausal models in finite samples for different values of the excess kurtosis of the error process. We compare the performance of the MLE, assuming a t-distribution, with that of theLAD estimator that we propose in this paper. Similar to Davis, Knight and Liu (1992) we find that for infinite variance autoregressive processes both the MLE and LAD estimator converge faster. We further specify the general asymptotic normality results obtained in Andrews, Breidt and Davis (2006)for the case of t-distributed and Laplacian distributed error terms. We first illustrate our analysis by estimating mixed causal-noncausal autoregressions to model the demand for solar panels in Belgium over the last decade. Then we look at the presence of potential noncausal components in daily realizedvolatility measures for 21 equity indexes. The presence of a noncausal component is confirmed in both empirical illustrations.

A new bootstrap procedure to obtain prediction densities of returns and volatilities of GARCH processes is proposed. Financial market participants have shown an increasing interest in prediction intervals as measures of uncertainty. Furthermore, accurate predictions of volatilities are critical for many financial models. The advantages of the proposed method are that it allows incorporation of parameter uncertainty and does not rely on distributional assumptions. The finite sample properties are analyzed by an extensive Monte Carlo simulation. Finally, the technique is applied to the Madrid Stock Market index, IBEX-35. Acknowledgements: We are very grateful for their helpful comments by three anonymous referees, the editor Stephen Pollock and seminar participants at the Universities of Valladolid, New South Wales and Canterbury and the June 2001 Time Series Workshop of Arrabida, the September 2001 International Conference on Modelling Volatility (Perth) and the June 2002 International Symposium on Forecasting (Dublin). We are also grateful to Gregorio Serna for providing the data set analyzed in this paper and to Dolores Redondas for helping us with the figures. Financial support was provided by projects DGES PB96-0111 and BEC2002-03720 from the Spanish Government and Cátedra de Calidad from BBVA Publicado

In this paper, we propose a bootstrap procedure to construct prediction intervals for future values of a variable after a linear ARIMA model has been fitted to its power transformation. The procedure is easy to implement and provides a useful tool in empirical applications given that it is often the case that, for example, the log-transformation is modeled when the variable of interest for prediction is the original one. The advantages over existing methods for computing prediction intervals of power-transformed time series are that the proposed bootstrap intervals incorporate the variability due to parameter estimation and do not rely on distributional assumptions neither on the original variable nor on the transformed one. We derive the asymptotic distribution and show the good behavior of the bootstrap approach versus alternative procedures by means of Monte Carlo experiments. Finally, the procedure is illustrated by analyzing three real-time series data sets. The authors are very grateful to Lutz Kilian for providing the RXR and NBRX series and to the associate editor Antonio García Ferrer and two anonymous referees for valuable comments that have been very helpful to improve the paper. Financial support was provided by projects DGES PB96-0111 and BEC 2002-03720 from the Spanish Government and Catedra de Calidad from BBV. Publicado

In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving-average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finite-sample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with moving-average components. Publicado