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espanolEn este trabajo se propone un test (no parametrico pero de calculo intensivo) de permutacion para evaluar la significacion estadistica del espectro wavelet de Foster mediante simulaciones de Monte Carlo. Un procedimiento (algoritmo) se introduce para llevar a cabo esta tarea. Los wavelet de Foster son un metodo adecuado para analizar directamente series paleoclimaticas irregulares. Se simularon series temporales con conocida informacion espectral (eventos periodicos) con el objeto de evaluar el desempeno en la deteccion de eventos periodicos conocidos a priori, incrementando el porcentaje de datos faltantes de manera aleatoria (desde un 25% a un 75% de la cantidad total de datos de una serie de control equiespaciada). Se encontro que ante la presencia de una gran cantidad de datos faltantes (lo cual es evidente desde un 50% y mas pronunciado con un 75%), las senales periodicas no se detectan en el espectro wavelet. Esto es mas evidente en las senales de corta frecuencia debido a la existencia de un sesgo en el espectro wavelet de Foster. Sin embargo, a pesar de lo anterior, el espectro wavelet de Foster en combinacion con el test de permutacion detectan adecuadamente senales periodicas en series sinteticas (simuladas) y reales con una moderada cantidad de datos faltantes. Finalmente, se aplico este metodo a valores medios de δ18O de los testigos de hielo del GISP2 (Groenlandia) y se encontro la principal caracteristica espectral de estos registros, esto es, la senal espectral ca. 1470 anos. EnglishHere we propose a permutation test -a non-parametric computing-intensive test- to evaluate the statistical significance of the Foster’s wavelet spectrum by means of Monte Carlo simulations. A procedure (algorithm) is introduced in order to carry out this aim. The Foster’s wavelet is an adequate method to cope directly with unevenly spaced paleoclimatic time series. We have conducted time series simulations to study the performance of the Foster’s wavelet spectrum and applied the permutation test to localize periodic signals known a priori by randomly increasing the fraction of missing data (from 25% to 75% of the total amount of data of an evenly spaced time series). We found that the periodic signals are progressively lost as larger amounts of data are removed. This loss becomes noticeable at circa 50% of the missing data and gets more evident when 75% of the data is removed. The signal loss is more pronounced in the high-frequency range, due to an intrinsic bias in the wavelet spectrum. Notwithstanding, the Foster’s wavelet spectrum and the permutation test succeeded in locating the periodic signals, even with a moderate amount of missing data. Finally, we applied our procedure to the oxygen isotope ratio (δ18O) data of the GISP2 deep ice core (Greenland) and we were able to detect the main spectral signature of the unevenly spaced time series of the GISP2 δ18O record, i.e., the spectral peak around 1,470 years.

Estimation of the significance of the Foster’s wavelet spectrum by means of a permutation test and its application for paleoclimate record