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The need to consider data that contain information that cannot be represented by classical models has led to the development of symbolic data analysis (SDA). As a particular case of symbolic data, symbolic interval time series are interval-valued data which are collected in a chronological sequence through time. This paper presents two approaches to symbolic interval time series analysis. The first approach is based on artificial neural networks. The second, is a new model based on exponential smoothing methods, where the smoothing parameters are estimated by using techniques for nonlinear optimization problems with bound constraints. The practicality of the methods is demonstrated by applications on real interval time series.