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

Abstract

Here 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 (δ 18 O) 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 δ 18 O record, i.e., the spectral peak around 1,470 years.

Mid- to Late-Holocene Mediterranean climate variability: Contribution of multi-proxy and multi-sequence comparison using wavelet spectral analysis in the northwestern Mediterranean basin

“…The aim of this article is to compare paleoclimatic time series in the frequency domain in order to identify similar patterns of variability and to draw connections between distinct climate proxies. To this end, we used spectral analysis methods specifically adapted to deal with irregularly sampled time series, as the resampling with constant time-steps can introduce unpredictable biases in the results (Schulz and Stattegger 1997, Schulz and Mudelsee 2002, Witt and Schumann 2005, Pardo-Igúzquiza and Rodríguez-Tovar 2012, Polanco-Martínez and Faria 2018, Lenoir and Crucifix 2018a.…”

“…Their application to paleoclimatic time series has highlighted the importance of nonstationarities to understand past climate variability (e.g. Witt and Schumann 2005, Polanco-Martinez andFaria 2018) RCCs are detected by means of numerous proxies all over the Mediterranean basin: vegetation changes (e.g.…”

Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

“…Particularly, the Point-Measure Enhancements (PME), the Intensity-Scale Skill Score (ISS) and the Wavelet Coefficient Score (WCS) were developed. Polanco-Martínez and Faria [30] used the wavelet transform in order to analyze the oxygen isotope ratio of the GISP2 deep ice core (Greenland) data. In fact, to evaluate the statistical significance of the Foster's wavelet spectrum, a non-parametric computing-intensive test was developed based on the Monte Carlo simulations.…”

Búsqueda de señal orbital en isótopos estables de carbono y oxígeno de belemnites del Jurásico Inferior de la cuenca Vasco-Cantábrica mediante el periodograma suavizado de Lomb-Scargle

“…Una posible solución para enfrentar el carácter no equiespaciado de las series temporales paleoclimáticas es interpolar en el tiempo y, así, obtener una serie temporal equiespaciada. Sin embargo, la interpolación implica un conocimiento previo del comportamiento de la variable de estudio, y suaviza los datos de tal modo que al calcular el espectro puede suprimir información espectral en las altas frecuencias (Schulz & Stattegger, 1997;Schulz & Mudelsee, 2002;Pardo-Iguzquiza & Rodríguez-Tovar, 2012;Polanco-Martínez, 2014;Polanco-Martínez & Faria, 2018). Otra solución consiste en utilizar métodos de análisis espectral que puedan aplicarse directamente (sin previa interpolación en el tiempo) a las series temporales paleoclimáticas, tales como el periodograma suavizado de Lomb-Scargle (Lomb 1976;Scargle 1982Scargle , 1989Schulz & Stattegger, 1997;Schulz & Mudelsee, 2002;Pardo-Igúzquiza & Rodríguez-Tovar 2011;Polanco-Martínez, 2014).…”