Jesus Miguel

Bootstrapping forecast intervals in ARCH models

In this paper we develop a bootstrap method for the construction of prediction intervals for an ARMA model when its innovations are an autoregressive conditional heteroscedastic process. We give a proof of the validity of the proposed bootstrap for this process. For this purpose we prove the convergence to zero in probability of the Mallows metric between the empirical distribution function and the theoretical distribution function of the residuals. The potential of the proposed method is assessed through a simulation study.

Adjusting Forecast Intervals in Arch-M Models

In this paper, we extend predictor expressions from an ARMA model with GARCH(1,1) innovations that allow for the conditional variance to be a regressor variable. We also obtain all the theoretical moments of the multi-step prediction error distribution from this model. The forecast error has a distribution that depends nontrivially on the information set and, therefore, the classical forecast intervals do not work well. To improve those forecast intervals, we suggest adjusting the quantile of the conditional distribution for the s-step-ahead forecast error by means of the Cornish-Fisher asymptotic expansion.

Evaluating value at risk using selection criteria of the model and the information set

This article proposes a new methodology to estimate the Value at Risk (VaR) in a time varying heteroscedastic dynamic regression context. The methodology assumes that the form of the model and its information set may also change over time and takes into account the uncertainty associated with the joint selection of model and information set, providing more reliability to the elaborated forecasts. A Bayesian framework is adopted and a cross validation selection criterion, asymptotically equivalent to the Bayes factor, is proposed. Finally, we estimate the VaR on line of five international equity indexes. Our VaR estimations tend to follow the evolution of the series more closely than classical procedures by keeping the coverage properties.

Testing heteroscedasticity: are parametric ARCH models appropriate?

Many researchers have used parametric ARCH models to specify the conditional variance of financial series. However, the usual tests do not provide any information on the form of the conditional variance. The objective of this paper is to present a test for heteroscedasticity, i.e. to decide whether the use of the parametric model can be justified. The test statistic is based on the distance between a non-parametric and a parametric estimator for the conditional variance. The critical values are calculated using a bootstrap method.