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Agrociencia
versão On-line ISSN 2521-9766versão impressa ISSN 1405-3195
Agrociencia vol.40 no.2 Texcoco Mar./Abr. 2006
Matemáticas Aplicadas, Estadística y Computación
Pruebas de bondad de ajuste para el movimiento browniano
1Estadística. Campus Montecillo. Colegio de Postgraduados. 56230. Montecillo, Estado de México. (jvillasr@colpos.mx)
En el análisis de series de datos financieros que ocurren en el tiempo, es importante verificar la suposición de que los datos pueden modelarse por un proceso de movimiento Browniano con el propósito de calcular el precio de instrumentos financieros de riesgo, llamados derivados. Con base en las propiedades del proceso Browniano, se proponen tres pruebas de bondad de ajuste del tipo unión-intersección. Se realizó un estudio de simulación de Monte Carlo para comparar las potencias de las pruebas para algunas hipótesis alternativas dadas de procesos no Brownianos, y diferentes tamaños de series de datos. Los resultados obtenidos muestran que, en general, las tres pruebas propuestas preservan el tamaño fijado; la prueba basada en la combinación de rachas, Shapiro-Wilk y t resultó ser en general la más potente respecto a las alternativas estudiadas y para casi todos los tamaños de series de datos considerados. Se hicieron aplicaciones a conjuntos de datos financieros.
Palabras clave: Aleatoriedad; datos financieros; procesos Gaussianos; pruebas estadísticas
In time series analyses of financial data it is important to verify the assumption that the data can be modeled by a Brownian movement process to calculate the price of the risky financial instruments called derivatives. Based on the properties of the Brownian process, three union-intersection-type goodnessof-fit tests are proposed. A Monte-Carlo simulation study was conducted to compare the power of the tests for some given alternative hypotheses of non-Brownian processes and different sizes of data series. The findings show that, in general, the three proposed tests preserve the assigned size; the test based on a combination of runs, Shapiro-Wilk and t, showed to be, in general, the most powerful against the studied alternatives and for almost all the data series sizes considered. Applications were performed on financial data sets.
Key words: randomness; financial data; Gaussian processes; statistical tests
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Recibido: Noviembre de 2003; Aprobado: Diciembre de 2005
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
