Trend smoothness achieved by penalized least squares with the smoothing parameter chosen by optimality criteria |
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Authors: | Daniela Cortés-Toto Víctor M Guerrero Hortensia J Reyes |
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Institution: | 1. Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla. Puebla, Puebla, México;2. Departamento de Estadística, Instituto Tecnológico Autónomo de México (ITAM). México, D.F., México |
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Abstract: | This work presents a study about the smoothness attained by the methods more frequently used to choose the smoothing parameter in the context of splines: Cross Validation, Generalized Cross Validation, and corrected Akaike and Bayesian Information Criteria, implemented with Penalized Least Squares. It is concluded that the amount of smoothness strongly depends on the length of the series and on the type of underlying trend, while the presence of seasonality even though statistically significant is less relevant. The intrinsic variability of the series is not statistically significant and its effect is taken into account only through the smoothing parameter. |
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Keywords: | Hodrick-Prescott filter Penalized least squares Percentage of smoothness Smoothing parameter Time series decomposition Trend estimation |
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