Maximum entropy spectral analysis of uneven time series in the geosciences

Eulogio Pardo-Igúzquiza; Peter A. Dowd

doi:10.21701/bolgeomin.131.2.007

Autores/as

Eulogio Pardo-Igúzquiza Instituto Geológico y Minero de España
Peter A. Dowd The University of Adelaide

DOI:

https://doi.org/10.21701/bolgeomin.131.2.007

Palabras clave:

máxima entropía, autorregresivo, datos perdidos, hiato, test de permutación

Resumen

Las series temporales con un intervalo de muestreo no constante aparecen con mucha frecuencia en Ciencias de la Tierra. Esto se debe a que el muestro ha podido ser aleatorio, o porque ha habido fallos en la toma de datos, hiatos, o por la transformación de una escala espacial (sondeo, columna estratigráfica, …) a una escala temporal cuando las tasas de sedimentación no son constantes. El método preferido para el análisis espectral de estas series temporales con muestreo irregular son los métodos que no requieren de una interpolación explícita de la seria para pasar a un muestreo regular, sino que tratan directamente los datos con espaciado no constante y, de entre estos métodos, el periodograma de Lomb-Scargle ha sido una elección muy frecuente por parte de los investigadores. En el trabajo aquí presentado, el estimador de máxima entropía, modificado para tratar con series temporales con muestreo no constante, se propone como una alternativa al periodograma. El atractivo de la metodología que se propone es que el estimador de máxima entropía es un estimador de alta resolución. El método propuesto aprovecha la equivalencia que existe entre el estimador espectral de máxima entropía y el estimador espectral autorregresivo. Además, se utiliza el test de permutación para evaluar el nivel de confianza estadístico de espectro de potencia estimado. Asimismo, se utilizan series temporales reales y simuladas para ilustrar el resultado de aplicar la metodología propuesta. Este trabajo muestra que el estimador de máxima entropía para series temporales irregulares evita los problemas de los lóbulos laterales que plagan las estimaciones por el periodograma de Lomb-Scarge mientras que se mantiene la alta resolución del estimador espectral de máxima entropía para series temporales cortas. Los resultados con el estimador de máxima entropía han resultado ser satisfactorios en los casos en los que importantes proporciones de los datos se han perdido al azar, cuando hay huecos a intervalos regulares en la serie de datos, cuando hay uno o más hiatos en la serie así como para series donde el muestreo ha sido aleatorio.

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Citas

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