AJUSTE DE UN MODELO NO LINEAL A LA VARIABLE PRECIPITACIÓN EN UNA ESTACIÓN HIDRO-METEOROLÓGICA DE COLOMBIA

FITTING A NONLINEAR MODEL TO THE PRECIPITATION VARIABLE IN A COLOMBIAN HYDROLOGICAL/METEOROLOGICAL STATION

En la literatura sobre análisis de series temporales, se ha establecido en años recientes que las series hidrológicas y meteorológicas se describen apropiadamente por modelos no lineales, en particular por los modelos SETAR (Self-exciting threshold autoregressive models). Combinamos dos métodos propuestos en la literatura para ajustar un modelo SETAR a datos de precipitación, medida en una estación hidro-meteorológica de Colombia.

In the literature on time series analysis it has been established in recent years that the hydrological/meteorological time series are well described by nonlinear models, in particular by the SETAR (Self- exciting threshold autoregressive) models. In this paper, a nonlinear SETAR model is fitted to the precipitation variable that is observed in a certain Colombian hydrological/meteorological station. In the fitting process, two alternative methodologies, which have been proposed in the literature about nonlinear time series models, are combined.

Ajuste de un modelo no lineal a la variable precipitación en una estación hidro-meteorológica de Colombia Fitting a nonlinear model to the precipitation variable in a Colombian hydrological/meteorological station ÁNGELA P. BRIÑEZ¹, FABIO H. NIETO²

¹Estadística de la Universidad Nacional de Colombia. E-mail:apbrinezr@unal.edu.co
²Profesor Titular, Departamento de Estadística de la Universidad Nacional de Colombia. E-mail: fhnietos@unal.edu.co

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Resumen

En la literatura sobre análisis de series temporales, se ha establecido en años recientes que las series hidrológicas y meteorológicas se describen apropiadamente por modelos no lineales, en particular por los modelos SETAR (Self-exciting threshold autoregressive models). Combinamos dos métodos propuestos en la literatura para ajustar un modelo SETAR a datos de precipitaci ón, medida en una estación hidro-meteorológica de Colombia.

Palabras Clave: Modelos SETAR, series de tiempo no lineales, precipitaci ón

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Abstract

In the literature on time series analysis it has been established in recent years that the hydrological/meteorological time series are well described by nonlinear models, in particular by the SETAR (Self- exciting threshold autoregressive) models. In this paper, a nonlinear SETAR model is fitted to the precipitation variable that is observed in a certain Colombian hydrological/ meteorological station. In the fitting process, two alternative methodologies, which have been proposed in the literature about nonlinear time series models, are combined.

Keywords: SETAR models, Nonlinear Time Series, Precipitation

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Referencias

1. Gomez, V. & Maravall, A. (1996), Programs TRAMO and SEATS: Instructions for the user, Banco de España-Servicio de estudios, Madrid.

2. Nieto, F. (2002), Interpolation of nonlinear TAR models., Unidad de Investigación, Departamento de Estadística, Universidad Nacional de Colombia, Bogotá. Reporte Interno No. 1.

3. Nieto, F. & Ruiz, F. (2002), "About a prompt strategy for estimating missing data in long time series", Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 100(26), 411- 418.

4. Tong, H. (1990), Nonlinear Time Series, A Dynamical System Approach, Oxford University Press, Oxford.

5. Tsay, R. S. (1989), "Testing and modeling threshold autoregressive processes", Journal of the American Statistical Association 84, 231- 240.