Exponential smoothing methods for forecasting bar diagram-valued time series

• Published in: 2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC) pp. 1361 - 1366
• Main Authors: de Araujo Junior, C.A.G., de Carvalho, F.A.T., Maia, Andre Luis Santiago
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2012
• Subjects: Accuracy; bar diagram-valued data; exponential smoothing; Forecasting; Predictive models; Smoothing methods; Time series analysis; Time series forecast; Training
• ISBN: 9781467317139; 1467317136
• ISSN: 1062-922X; 2577-1655
• DOI: 10.1109/ICSMC.2012.6377923

When a set of categories with related frequencies of the observed variable is available for each time point we have a bar diagram-valued time series. This paper introduces exponential smoothing methods to forecast bar diagram-valued time series data. The proposed method is inspired in the approach introduced by Maia and De Carvalho (2011) to deal with inteval-valued time series. The smoothing parameters are estimated by using techniques for non-linear optimization problems with bound constraints. The results are discussed based on two wellknown classical performance measurements, which have been adapted here for this particular type of data: the U of Theil statistics and average relative variance (ARV) in the framework of a Monte Carlo experiment. The synthetic data sets take into account differents aspects, e.g., sample size and forecast horizons among others. Applications using real bar diagram-valued time series also were considered to demonstrate the practicality of the methods. The results demonstrate that the proposed approaches are useful in forecasting bar diagram-valued times series.