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WaveletComp 1.1: A guided tour through the R package
Abstract and Figures
WaveletComp is an R package for continuous wavelet-based analysis of univariate and bivariate time series. Wavelet functions are implemented in WaveletComp such that a wide range of intermediate and final results are easily accessible. The null hypothesis that there is no (joint) periodicity in the series is tested via p-values obtained from simulation, where the model to be simulated can be chosen from a wide variety of options. The reconstruction, and thus filtering, of a given series from its wavelet decomposition, subject to a range of possible constraints, is also possible. WaveletComp provides extended plotting functionality — which objects should be added to a plot (for example, the ridge of wavelet power, contour lines indicating significant periodicity, arrows indicating the leading/lagging series), which kind and degree of smoothing is desired in wavelet coherence plots, which color palette to use, how to define the layout of the time axis (using POSIXct conventions), and others. Technically, we have developed vector- and matrix-based implementations of algorithms to reduce computation time. Easy and intuitive handling was given high priority.
Even though we provide some details concerning the mathematical foundation of the methodology implemented in WaveletComp, the present guide is not intended to give an introduction to wavelet analysis. The goal here is to give a series of constructed as well as real-world examples to illustrate the use and functionality of WaveletComp, with statistical arguments in mind.
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... A 95% confidence level for wavelet analysis was conducted through a Monte Carlo Simulation. Wavelet analysis was done using the 'WaveletComp' package (Schmidbauer & Roesch, 2018) ...
... A 95% confidence level for the CWT was done through Monte-Carlo simulation using 1000 times. In this study, wavelet analysis was done using 'WaveletComp' package (Schmidbauer & Roesch, 2018) in R (R Core Team, 2019). ...
Increases in dissolved organic carbon (DOC) concentrations, or browning,
have occurred in many freshwater ecosystems across Europe and North
America in recent decades, giving the water a brownish color. Several
mechanisms have been proposed to explain aquatic browning, but
consensus regarding the relative importance of recovery from acid
deposition, climate change, and land management remains elusive.
Meanwhile, elevated CO2, longer growing seasons and permafrost thaw
induced by climate change have increased terrestrial productivity, which
may alter the export of DOC from terrestrial to aquatic ecosystems.
Although the link between terrestrial greening and aquatic browning has
recently gained more attention, it is not yet well established. Moreover,
heterogeneities of browning across space and time have been observed, but
the reasons behind these differences are still unclear.
The objectives of this thesis are to understand how varied factors affect
short–term variations and long–term trends of DOC concentrations in boreal
catchments, focusing especially on the nexus between terrestrial carbon (C) export and stream DOC concentrations, and the causes of spatial and
temporal heterogeneity in browning across boreal catchments. The thesis is
based on three studies. Study I developed methods to predict real–time
high-frequency DOC concentrations in catchments using in–situ UV–Vis
spectrophotometers, which can be applied especially in remote areas to
save time and money. Study II used the methods developed by Study I to
predict high–resolution time series DOC concentrations and analysed the
relationship between terrestrial productivity and short–term DOC variations
across boreal catchments. Study III extended the analysis to longer time
periods and wider range catchments by integrated mechanisms (recovery
from acid deposition, climate change, and site characteristics), quantified
the contributions of multiple drivers on long–term DOC trends and provided
an explanation for the spatiotemporal heterogeneity of browning.
Collectively, this thesis revealed that increased terrestrial productivity
induced by climate change can alter terrestrial DOC exports to aquatic
ecosystems through priming effect. Whereas no single mechanism can fully
explain long–term DOC trends; instead, recovery from sulfate deposition,
terrestrial productivity, discharge, and temperature jointly shaped DOC
trends. Site characteristics (catchment size and land cover type) can affect
the response rate of DOC to these drivers leading to the spatial
heterogeneity of browning across sub–catchments. Moreover, browning has
weakened in the last decade as sulfate deposition has fully recovered and
other current drivers are insufficient to sustain the long–term DOC trends.
My work improves our mechanistic understanding of surface water DOC
regulation in boreal catchments, confirms the importance of DOC fluxes in
regulating ecosystem C budgets and highlights the significance of
considering multifaceted, spatially structured, and nonstationary drivers
when predicting long–term DOC trends in the future.
... As such, the continuous wavelet analysis can detect variations in the dominant dive cycle periodicities across the time series (Cazelles et al. 2008), or intra-individual variability in the temporal patterns of diving behaviour. Moreover, another benefit of the continuous wavelet analysis is that it can be used to evaluate a customisable range of temporal periodicities, on the order of minutes to days depending on the length of the time-series intervals and the objectives (Rösch and Schmidbauer 2018). ...
... The continuous wavelet analysis was completed using the R package WaveletComp (ver. 1.1, A. Rösch and H. Schmidbauer, see https://CRAN.R-project.org/package=WaveletComp). Based on the temporal resolution of our data, periodicities of interest and related previous work (Thorburn et al. 2019;Burke et al. 2020) parameters were set as follows: a loess span of 0, a sampling resolution of 0.5 h, a frequency resolution of 1/250, a lower period for the wavelet function of 1 h, an upper period for the wavelet function of 128 h, and the number of simulations of 100 (details in Rösch and Schmidbauer 2018). The continuous wavelet analysis returns a plot of the wavelet power spectrum, which identifies dominant dive periodicities (h; y-axis) over the duration of the tag deployment (x-axis). ...
Context: For threatened marine species, data on their vertical habitat use patterns can reveal risk of interactions with fishing gear and can inform bycatch avoidance strategies. Such data are lacking for young porbeagles (Lamna nasus), which are captured as bycatch in northwestern Atlantic fisheries. Aims: We aimed to examine temporal patterns in diving and characterise vertical habitat use of young porbeagles during summer and autumn. Methods: We used data from short-term (28-day), high-resolution (5-min interval) pop-off satellite tags attached to 14 young (young-of-the-year and 1-year-old) porbeagles to model depth use. Key results: Occupied depths ranged from the sea surface to 679 m, with ambient water temperatures of −0.2 to 26°C. Diel period and season were factors related to depth use. Conclusions: Sharks exhibited a diel activity pattern characterised by more extensive use of the water column during the day while remaining primarily at the surface at night. Depth use differed between seasons, with summer characterised by greater affinity for surface waters (0-10 m) compared to autumn. Implications: Young porbeagles are at risk of interaction with active fisheries on the continental shelf, but interactions may be reduced by setting gear deeper at night or during summer.
... The cone-like shape represents cone of influence and the area outside it is not interpreted. - (Rösch & Schmidbauer, 2016). ...
Time-frequency domain analysis of housing prices can provide insights into significant periodic patterns in the pricing dynamics for modelling and forecasting purposes. This study applied wavelet and information entropy analyses to examine the periodic patterns and evolution of housing prices in Australia’s eight capital cities from 1980 to 2023, using quarterly median house pricing data. Our findings revealed consistent patterns of higher variability in housing prices at high frequencies across all cities, with Melbourne exhibiting the highest variability. This indicates that short-term price fluctuations were higher than long-term changes. Perth And Brisbane demonstrated notable cyclical patterns with recurring periods of growth and decline. Coherence analyses revealed dynamic lead–lag relationships, both positive and negative,between housing prices of various cities, suggesting interconnectedness but not always synchronisation. Some cities’ housing prices dominated the information sharing, indicating varying degrees of influence within the national market. These findings highlight the complex, dynamic interdependencies among Australia’s major city housing markets, providing valuable insights for policymakers,investors, and stakeholders in economic forecasting, policy development and strategic planning within these markets.
... y CWT de la biblioteca R WaveletComp (https://cran.r-project. org/web/packages/WaveletComp/index.html)[30]. ...
La concentración de clorofila-a en los océanos es un indicador confiable de biomasa de fitoplancton que desempeña un papel importante en el control del ecosistema marino. El objetivo principal de este estudio es analizar la variabilidad de la concentración de clorofila-a (Chl-a) y temperatura superficial del mar (TSM) en el ecosistema de afloramiento peruano en la escala de tiempo interanual, utilizando información satelital del sensor MODIS a bordo del satélite Aqua en el periodo de 2003 hasta 2021. El área de estudio está delimitada por la isobata de 1mg m−3 de clorofila-a y las latitudes de 5°S y 20°S, esta área se divide en dos zonas, norte-centro (5°S-16°S) y sur (16°S-20°S). Iniciamos investigando las tendencias lineales, donde los resultados indicaron que se produjeron tendencias negativas de los dos parámetros en el área de estudio, notando que para la TSM es mayor este enfriamiento en la zona norte-centro (≈-0.076°C década−1), en el caso de la Chl-a también muestra un mayor decrecimiento en la zona sur (≈-0.07 mg m−3 década−1). Para determinar el periodo de variabilidad interanual de cada parámetro usamos el análisis del espectro de potencia de wavelet (EPW) y para determinar el periodo común de los dos parámetros usamos la transformada de ondas cruzadas (CWT), ambos análisis son basados en la transformada wavelet, aplicamos estos análisis a la componente principal (PC1) de cada parámetro. Los resultados permitieron identificar que en la zona norte-centro el periodo significativo de cada uno de los parámetros es mayor a 3 años y en la zona sur los periodos significativos también son mayores a 3 años. En cuanto al periodo común de variabilidad interanual de los parámetros en la zona norte-centro es de 3.4 años y en la zona sur el periodo común es de 3.3 años. Estos periodos de variabilidad interanual (>3 años) de la TSM y Chl-a en toda el área de estudio son principalmente relacionados al ENSO, estos periodos tienen mayor energía en la zona norte-centro y menor energía en la zona sur esto estaría en concordancia con la disminución en amplitud y energía de la onda de Kelvin a medida que se propaga a lo largo de la costa peruana.
Context
Rapid increases in human population and the resulting apex predator defaunation are affecting the spatial and temporal dynamics of small carnivores, with uncertain consequences for the ecological community. Documenting the spatiotemporal impact of apex predators and human disturbance on small carnivores becomes crucial to managers overseeing carnivore persistence.
Objectives
Assessing the spatiotemporal responses of five small carnivores to two apex carnivores (tigers Panthera tigris, leopards P. pardus) and human disturbances in Northeast Asia.
Methods
We first applied an occupancy-modelling framework to test whether site occupancy of small carnivores depended on apex carnivore and human disturbance. Then, we calculated the overlap of activity periods between small carnivores and apex predators, as well as the overlap with human/cattle activities using kernel density functions. Finally, we used cross-wavelet analysis to determine the temporal coherence between related species.
Results
Spatially, most small carnivores were independent of tigers and leopards. Compared to apex predators, small carnivores were more likely to use areas with high human activity. Temporally, small carnivores exhibited highly heterogeneous diel overlaps and more in-phase activities with apex predators. However, we found a significant difference in the mean activity time between apex and small carnivore. Meanwhile, small carnivores exhibited low levels of temporal overlap and more out-phase temporal coherence with humans and cattle at shorter periods.
Conclusions
Apex carnivores and human disturbances don’t limit the space use or intensity of use of small carnivores. Temporal segregation and anti-phase activity are the key role for small carnivores to minimize intraguild predation and human persecution.
Bu makale, avro bölgesindeki 7 ülkede (Belçika, Fransa, Yunanistan, İtalya, Portekiz ve İspanya) kamu borcu ile ekonomik büyüme arasındaki ilişkiyi 2000Ç1'den 2023Ç3'e kadar dalgacık analizi kullanarak incelemektedir. Çapraz dalgacık gücü ve dalgacık tutarlığı tahmin sonuçlarına göre, incelenen dönemde kamu borcu ile ekonomik büyüme arasındaki ilişkinin hem kısa (0.5-2 çeyreklik frekans) hem de uzun ölçeklerde (2-4 arası çeyreklik frekans) yüksek korelasyon gösterdiği tespit edilmiştir. Her iki analiz sonucunda, muhtelif dönem ve frekanslar için ülkelerin sonuçları birbirinden farklı çıksa da genel olarak kamu borcu ve ekonomik büyüme arasındaki ilişki negatif yönlüdür. Ayrıca, çapraz dalgacık gücü tahmin sonuçlarına göre, 2018-2022 döneminde İtalya, Yunanistan ve Fransa’da kısa dönemde yapılan borçlanmanın ekonomik büyümeyi teşvik ettiği fakat uzun dönemde ise bazı ülkelerde ekonomik büyümenin negatif etkilendiği görülmüştür. Ek olarak, Avrupa borç krizi ve korona virüs pandemi döneminde ülkelerin ortaya koyduğu kamu borç-ekonomik büyüme ilişkisi birbirleri ile senkronize hareket ettiği görülmekle birlikte bu dönemde, neoklasik görüşün geçerli olduğunu ortaya konulmuştur. Sonuç olarak, özellikle borç kriz dönemlerinde, politika yapıcılarının ekonomik büyümeyi olumsuz etkileyen kamu borcunu azaltmaya yönelik mali kuralları belirlemesi gerektiği ortaya çıkmıştır.
This paper aims to study the relationship between producer price index (PPI) and consumer price index (CPI), as well as between components of producer prices and components of consumer prices in Azerbaijan by using monthly data covering the period from March 2004 to June 2023. Applying wavelet analysis approach, I find that there is a mixed relationship between CPI and PPI, and co-movement is observed mainly at medium and low frequencies. The results reveal that although there is a weak co-movement between aggregate PPI and CPI, a significant and strong relationship exists between food PPI and aggregate CPI, as well as between food PPI and food CPI. Additionally, producer prices of agricultural products demonstrates comovement with consumer prices in certain periods. In terms of lead-lag relationship, producer prices lead consumer prices. Although wavelet methodology does not necessarily determine causality, this study provides insights for policymakers about the direction of possible causality between producer prices and consumer prices.
The cross wavelet transform (XWT) is a powerful tool for testing the proposed connections between two time series. Because of XWT’s skeletal structure, which is based on the wavelet transform, it is suitable for the analysis of non-stationary periodic signals. Recent work has shown that the power spectrum based on the wavelet transform can produce a deviation, which can be corrected by choosing a proper rectification scale. In this study, we show that the standard application of the XWT can also lead to a biased result. A corrected version of the standard XWT was constructed using the scale of each series as normalizing factors. This correction was first tested in an artificial example involving two series build from combinations of two harmonic series of different amplitudes and frequencies. The standard XWT applied to this example produce a biased result, whereas the correct result is obtained with used of the proposed normalization. This analysis was then applied to a real geophysical situation with important implications to climate modulation on the northwestern Brazilian coast. The linkage between the relative humidity and the shortwave radiation measurements, obtained from the 8°S 30°W ATLAS buoy of the Southwestern Extension of the Prediction and Research moored Array in the Tropical Atlantic Project (PIRATA-SWE), was explored. The analysis revealed the importance of including the correction in order to not overlook any possible connections. The requirements of incorporating this correction in the XWT calculations are emphasized.
The present study is an effort to analyze the timing of media postings related to candidates Clinton and Trump on Instagram before and after the 2016 US presidential election. Hashtags are used to determine whether a posting was intended to support or oppose either candidate. We thus obtain four hourly time series: Clinton vs. Trump, supporters vs. opponents. Based on cross-wavelet analysis, we find that, at the 12-h period, Trump supporters were leading Trump opponents as well as Clinton supporters the days before the election, while Clinton opponents were often leading Clinton supporters: Trump supporters and Clinton opponents were eager to post media, while Trump opponents and Clinton supporters were sluggish. Considering election forecasts, our results come as a surprise.
A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El NiñoSouthem Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of changes in ENSO variance on interdecadal timescales. Using new datasets that extend back to 1871, the Niño3 sea surface temperature and the Southern Oscillation index show significantly higher power during 1880-1920 and 1960-90, and lower power during 1920-60, as well as a possible 15-yr modulation of variance. The power Hovmöller of sea level pressure shows significant variations in 2-8-yr wavelet power in both longitude and time.
We use wavelet analysis to study business cycle synchronization across the EU-15 and the Euro-12 countries. Based on the wavelet transform, we propose a metric to measure and test for business cycles synchronization. Several conclusions emerge. France and Germany form the core of the Euro land, being the most synchronized countries with the rest of Europe. Portugal, Greece, Ireland and Finland do not show statistically relevant degrees of synchronization with Europe. We also show that some countries (like Spain) have a French accent, while others have a German accent (e.g., Austria). Perhaps surprisingly, we find that the French business cycle has been leading the German business cycle as well as the rest of Europe. Among the countries that may, in the future, join the Euro, the Czech Republic seems the most promising candidate.
High-resolution seismic methods are needed especially in oil and gas field development. They involve the use of backscattered energy rather than that of reflected signals, and make it interesting to look for representations of seismic traces in the time-frequency domain. One such representation was introduced by D. Gabor in 1946 into signal analysis; it is based on the consideration of a family of “elementary wavelets” that can be obtained from one “basic wavelet” by shifts in time and in frequency. We present here a different representation, in which frequency shifts are replaced by dilations. The resulting “voice transform” and “cycle-octave transform” are briefly described from the mathematical point of view and illustrated by numerical examples.