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Keywords:

  • Bayesian methods;
  • density forecasts;
  • generalized lambda distribution;
  • quantile function;
  • quantile forecasts

ABSTRACT

We develop a novel quantile double autoregressive model for modelling financial time series. This is done by specifying a generalized lambda distribution to the quantile function of the location-scale double autoregressive model developed by Ling (2004, 2007). Parameter estimation uses Markov chain Monte Carlo Bayesian methods. A simulation technique is introduced for forecasting the conditional distribution of financial returns m periods ahead, and hence any for predictive quantities of interest. The application to forecasting value-at-risk at different time horizons and coverage probabilities for Dow Jones Industrial Average shows that our method works very well in practice. Copyright © 2013 John Wiley & Sons, Ltd.