¹Universidad Nacional de Colombia, Facultad de Ciencias, Medellín, Colombia. Universidad de Antioquia, Facultad de Ciencias Económicas, Medellín, Colombia. Profesor asociado, profesor titular. Email: elkincv@gmail.com
²Universidad Nacional de Colombia, Facultad de Ciencias Humanas y Económicas, Departamento de Economía, Medellín, Colombia. Profesor auxiliar. Email: kgomezp@unal.edu.co
³Universidad Nacional de Colombia, Facultad de Ciencias Humanas y Económicas, Departamento de Economía, Medellín, Colombia. Profesor auxiliar. Email: sgallong@unal.edu.co

Este documento presenta una nueva prueba para el parámetro de diferenciación fraccional de un modelo ARFIMA, basada en una aproximación autorregresiva de su componente a corto plazo. El comportamiento de la prueba se estudia por medio de experimentos Monte Carlo en una distribución normal, y se compara con el comportamiento de algunas de las pruebas más utilizadas. Para los casos estudiados, se concluye que la nueva prueba tiene generalmente potencias superiores, conservando un tamaño adecuado. A partir de la estimación del parámetro de diferenciación fraccional usando el modelo aproximado, es posible identificar el modelo correcto para la componente a corto plazo, lo cual permite mejorar la inferencia sobre dicho parámetro. Una ventaja adicional del procedimiento propuesto es que permite probar la existencia de larga memoria en presencia de errores dependientes, como en el caso de modelos de volatilidad de la familia ARCH. Se ilustra su aplicación en un procedimiento de identificación y estimación de un modelo ARFIMA--ARCH usando datos simulados.

Palabras clave: memoria larga, modelo ARFIMA, aproximación autorregresiva, identificación, prueba de hipótesis, diferencia fraccional.

This paper presents a new test for the fractional differencing parameter of an ARFIMA model, based on an autoregressive approximation of its short-range component. The tests behavior is studied using Monte Carlo simulations under a normal distribution and is compared to results found for others well--known long memory tests. In general, the results show that the new test has a superior power while maintaining an adequate size of the test. From the estimation of the fractional differencing parameter using the approximate model, it is possible to identify the correct model for the short--term component, which allows improving the inference on the above mentioned parameter. An additional advantage of the proposed procedure is the possibility of testing long memory in the presence of dependent errors such as in the volatility models of ARCH family. The identification and estimation procedure is applied to simulated data from an ARFIMA--ARCH model

Key words: Long memory, Arfima model, Autoregressive process, Identification, Testing hypothesis, Fractional differencing.

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