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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.33 no.1 Bogotá Jan./June 2010


Nonparametric Time Series Analysis of the Conditional Mean and Volatility Functions for the COP/USD Exchange Rate Returns

Análisis de series de tiempo no paramétrico de las funciones de media y varianza condicional de los retornos de la tasa de cambio COP/USD


1Universidad de Antioquia, Facultad de Ciencias Económicas, Departamento de Estadística y Matemáticas - Departamento de Economía, Medellín, Colombia. Universidad de Antioquia, Facultad de Ciencias Económicas, Grupo de Econometría Aplicada, Medellín, Colombia. Profesor asistente. Email:
2Universidad Nacional de Colombia, Facultad de Ciencias Humanas y Económicas, Departamento de Economía, Medellín, Colombia. Universidad de Antioquia, Facultad de Ciencias Económicas, Grupo de Econometría Aplicada, Medellín, Colombia. Profesor auxiliar. Email:


The modeling and estimation of the conditional volatility associated with a stochastic process usually have been based on parametric ARCH-type and stochastic volatility models. These time series models are very powerful in representing the dynamic stochastic properties of the data generating process only if the parametric functions are correctly specified. The nonparametric approach acquires importance as a complementary and flexible method to explore these properties without imposing particular functional forms on the conditional moments of process. This paper presents an application of nonparametric time series methods to estimate the conditional volatility function of the COP/USD exchange rate returns. Additionally, we estimate the conditional mean function under this approach.

Key words: Nonparametric regression, Local polynomial regression, Nonlinear time series, Variance function estimation, Autoregressive conditional heteroscedasticity, Time series analysis.


La modelación y estimación de la volatilidad condicional asociada a un proceso estocástico ha estado basada en los modelos paramétricos tipo ARCH y de volatilidad estocástica. Estos modelos son muy poderosos para representar las propiedades dinámicas estocásticas del proceso generador de datos solo si las funciones paramétricas están correctamente especificadas. En este sentido, el enfoque no paramétrico adquiere importancia como un método complementario y flexible para explorar dichas propiedades al no imponer formas funcionales particulares en los momentos condicionales del proceso. Este documento presenta una aplicación de los métodos no paramétricos de series de tiempo para estimar la función de volatilidad condicional de los retornos de la tasa de cambio COP/USD. Además, se estima la función de media condicional bajo este enfoque.

Palabras clave: regresión no paramétrica, regresión polinomial local, series de tiempo no lineales, estimación de la función de varianza, heterocedasticidad condicional autorregresiva, análisis de series de tiempo.

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[Recibido en null de 2009. Aceptado en null de 2010]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

    AUTHOR  = {Gallón, Santiago and Gómez, Karoll},
    TITLE   = {{Nonparametric Time Series Analysis of the Conditional Mean and Volatility Functions for the COP/USD Exchange Rate Returns}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2010},
    volume  = {33},
    number  = {1},
    pages   = {25-41}

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