Bootstrap based probability forecasting in multiplicative error models

As evidenced by an extensive empirical literature, multiplicative error models (MEM) show good performance in capturing the stylized facts of nonnegative time series; examples include, trading volume, financial durations, and volatility. This paper develops a bootstrap based method for producing multi-step-ahead probability forecasts for a nonnegative valued time-series obeying a parametric MEM. In order to test the adequacy of the underlying parametric model, a class of bootstrap specification tests is also developed. Rigorous proofs are provided for establishing the validity of the proposed bootstrap methods. The paper also establishes the validity of a bootstrap based method for producing probability forecasts in a class of semiparametric MEMs. Monte Carlo simulations suggest that our methods perform well in finite samples. A real data example illustrates the methods.