Modeling and forecasting interval time series with threshold models

This paper proposes threshold models to analyze and forecast interval-valued time series. A relatively simple algorithm is proposed to obtain least square estimates of the threshold and slope parameters. The construction of forecasts based on the proposed model and methods for the analysis of their forecast performance are also introduced and discussed, as well as forecasting procedures based on the combination of different models. To illustrate the usefulness of the proposed methods, an empirical application on a weekly sample of S&P500 index returns is provided. The results obtained are encouraging and compare very favorably to available procedures.

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