Modeling and forecasting interval time series with threshold models

The analyses, opinions and fi ndings of these papers represent the views of the authors, they are not necessarily those of the Banco de Portugal or the Eurosystem Abstract Over recent years several methods to deal with high-frequency data (economic, …nancial and other) have been proposed in the literature. An interesting example is for instance interval-valued time series described by the temporal evolution of high and low prices of an asset. In this paper a new class of threshold models capable of capturing asymmetric e¤ects in interval-valued data is introduced as well as new forecast loss functions and descriptive statistics of the forecast quality proposed. Least squares estimates of the threshold parameter and the regression slopes are obtained; and forecasts based on the proposed threshold model computed. A new forecast procedure based on the combination of this model with the k nearest neighbors method is introduced. To illustrate this approach, we report an application to a weekly sample of S&P500 index returns. The results obtained are encouraging and compare very favorably to available procedures. Acknowledgements: We thank participants of the ISF 2010 conference in San Diego for useful comments and suggestions.