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Bootstrap methods for inference and forecasting in multiplicative error models

The recent literature on time series analysis has devoted considerable attention to nonnegative time series, such as financial durations, realized volatility, and squared returns. The class of models, referred to as the Multiplicative Error Models (MEM), is particularly suited to model such nonnegative time series. A novel bootstrap-based method is proposed for producing multi-step-ahead probability forecasts for MEMs, including distributional forecasts. In order to test the adequacy of the underlying MEM, a class of bootstrap specification tests is also proposed. The proposed bootstrap methods are shown to be asymptotically valid. Monte Carlo simulations suggest that our methods perform well in finite samples. A real data example illustrates the methods.