ArticlePDF Available

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.
Content may be subject to copyright.
A preview of the PDF is not available
... The complex argument of W n XY can be interpreted as the local relative phase between time series X j and Y j . Thus, phase values less (larger) than π/2 indicates that the two series move in-phase (anti-phase, respectively), while the sign of the phase difference shows which series is the leading one in the relationship (Rösch and Schmidbauer, 2014). Statistical significance is estimated against a red noise model (Torrence and Compo, 1998). ...
... XWT reveals areas with high common power. Nevertheless, it depends on the unit of measurement of the series and may not readily interpretable with regard to the degree of association of the two series (Rösch and Schmidbauer, 2014). Wavelet coherence may remedy this, although it can find significant relationships even though the common power between series is low (Grinsted et al., 2004). ...
Article
Full-text available
This study identifies significant periodicities in streamflow dynamics across western Europe using a hydrological database encompassing 1874 monthly series from catchments in Ireland, the United Kingdom, France, Spain and Portugal, spanning the years 1962 to 2012. Significant and synchronous periodicities with the main atmospheric mechanisms over the North Atlantic sector are also identified using Cross Wavelet Transform and Wavelet Coherence analysis. Principal Components Analysis (PCA) were applied to the different Wavelet transforms analysis in order to summarize the results. These show the occurrence of a 7-years streamflow cycle in a large proportion of catchments within the study domain since the mid 1980’s that was not present in earlier periods. The significance, intensity and persistence of the observed regional cycle follows a spatial gradient around the English Channel. We show how the transitive coupling of key atmospheric mechanisms is an influencing factor causing the general change observed. These results suggest the occurrence of a regional change in the periodicities of streamflow across the western European domain. Our results emphasize the non-stationary interaction between streamflow and atmospheric circulation during recent decades and the prominent role of the North Atlantic Oscillation in the newly stablished streamflow cycles.
... To further characterize the behavioral rhythms in the entrained C. floridanus colony and to investigate the potential behavioral effects of the disturbance introduced by the mark-recapture, we performed wavelet analyses [76] on the foraging data collected during the four-day period just after mark-recapture and prior to sampling (Fig. 1, . Camponotus floridanus ants of the foraging caste showed significant 24 h-rhythms in feeding and foraging activity ( Fig. 2A). ...
... We confirmed daily rhythms in colony activity with the WaveletComp package [76]. Using wavelet analyses, we investigated the extranidal activity of foragers for the presence of 24 h-rhythms in colony behavior, the potential presence of ultradian rhythms, and to infer synchronicity between the number of ants actively feeding or present on the feeding stage (feeding activity), and those present in the remainder of the foraging arena (foraging activity). ...
Article
Full-text available
Background Circadian clocks allow organisms to anticipate daily fluctuations in their environment by driving rhythms in physiology and behavior. Inter-organismal differences in daily rhythms, called chronotypes, exist and can shift with age. In ants, age, caste-related behavior and chronotype appear to be linked. Brood-tending nurse ants are usually younger individuals and show “around-the-clock” activity. With age or in the absence of brood, nurses transition into foraging ants that show daily rhythms in activity. Ants can adaptively shift between these behavioral castes and caste-associated chronotypes depending on social context. We investigated how changes in daily gene expression could be contributing to such behavioral plasticity in Camponotus floridanus carpenter ants by combining time-course behavioral assays and RNA-Sequencing of forager and nurse brains. Results We found that nurse brains have three times fewer 24 h oscillating genes than foragers. However, several hundred genes that oscillated every 24 h in forager brains showed robust 8 h oscillations in nurses, including the core clock genes Period and Shaggy. These differentially rhythmic genes consisted of several components of the circadian entrainment and output pathway, including genes said to be involved in regulating insect locomotory behavior. We also found that Vitellogenin, known to regulate division of labor in social insects, showed robust 24 h oscillations in nurse brains but not in foragers. Finally, we found significant overlap between genes differentially expressed between the two ant castes and genes that show ultradian rhythms in daily expression. Conclusion This study provides a first look at the chronobiological differences in gene expression between forager and nurse ant brains. This endeavor allowed us to identify a putative molecular mechanism underlying plastic timekeeping: several components of the ant circadian clock and its output can seemingly oscillate at different harmonics of the circadian rhythm. We propose that such chronobiological plasticity has evolved to allow for distinct regulatory networks that underlie behavioral castes, while supporting swift caste transitions in response to colony demands. Behavioral division of labor is common among social insects. The links between chronobiological and behavioral plasticity that we found in C. floridanus, thus, likely represent a more general phenomenon that warrants further investigation.
... For the purpose of this paper, the terms wavelet analysis and wavelet coherence are used interchangeably. 10 For a detailed analysis see Rösch and Schmidbauer (2016). 11 A complete analysis of the Morlet wavelet and its application in finance can be found in Madaleno and Pinho (2010). ...
Preprint
Full-text available
In 2021, meme stocks attracted the attention of investors and scholars. Using Wavelet Coherence analysis, we test the dynamic interdependence between the AMC Theatres stock performance and the explanatory factors of Google Trends index, Put-Call ratio, and Trading Volume for the period 2018-2021. Our empirical findings suggest that during 2018-2020 the examined variables do not have stable co-movements with the AMC returns, but in the growth year of 2021 the relationships amongst the variables are stable and statistically significant. Thus, wavelet analysis is a useful tool that shows dynamically the impact relationships between several factors and the stock prices. Particularly, in 2021 the skyrocketing increase of the AMC stock price caught the attention of market participants and the AMC returns lead the Google searches with an in-phase synchronization (positive correlation). Moreover, AMC returns lead the Put-Call ratio, which is a sentiment indication from the derivatives market, and the Trading Volume positively correlates with the stock returns reconfirming once again the theoretical price-volume relation.
... A wavelet analysis was used to decompose a time series to reveal periodic signals at each time point in the series. The wavelet analysis coefficients show the correlation magnitudes of ENSO anomalies (NINO 3.4 index), temperature, or rainfall for each year and period length of the time series (i.e., 1993 to 2020), displayed using a power spectrum over the full time series using the biwavelet and WaveletComp packages [36,37] implemented in R [38]. The ccf function was then used to compute the cross-correlation or cross-covariance between univariate series, i.e., ENSO (NINO 3.4 index); the average monthly temperature; the average monthly rainfall; land surface temperature anomalies; and either HeV or NiV recurring spillover events in Australia and in Bangladesh, respectively. ...
Article
Full-text available
Climate variability and anomalies are known drivers of the emergence and outbreaks of infectious diseases. In this study, we investigated the potential association between climate factors and anomalies, including El Niño Southern Oscillation (ENSO) and land surface temperature anomalies, as well as the emergence and spillover events of bat-borne viral diseases in humans and livestock in the Asia–Pacific region and the Arabian Peninsula. Our findings from time series analyses, logistic regression models, and structural equation modelling revealed that the spillover patterns of the Nipah virus in Bangladesh and the Hendra virus in Australia were differently impacted by climate variability and with different time lags. We also used event coincidence analysis to show that the emergence events of most bat-borne viral diseases in the Asia–Pacific region and the Arabian Peninsula were statistically associated with ENSO climate anomalies. Spillover patterns of the Nipah virus in Bangladesh and the Hendra virus in Australia were also significantly associated with these events, although the pattern and co-influence of other climate factors differed. Our results suggest that climate factors and anomalies may create opportunities for virus spillover from bats to livestock and humans. Ongoing climate change and the future intensification of El Niño events will therefore potentially increase the emergence and spillover of bat-borne viral diseases in the Asia–Pacific region and the Arabian Peninsula.
... The quasi-annual periodicity was calculated from the original time series with wavelet transformation, while the multiyear periodicity was calculated from the time series after detrending seasonality. Wavelet power spectrum analysis was carried out using the package "WaveletComp" (Rösch & Schmidbauer, 2016) and "biwavelet" (Gouhier et al., 2018) in R. ...
Article
Vegetative and reproductive growth of subtropical and tropical forests plays an important role in regulating carbon cycle and maintaining food web dynamic balance. Here, we used litterfall and climatic data during 1998–2017 at four evergreen forest sites in southern China to analyze temporal variations of community phenology and their climate drivers. Results show that two southwest forests have unimodal patterns with leaf litterfall peaks during dry season, while two southeast forests have bimodal patterns with the first peaks during rainy season and the second peaks during rainy and dry seasons respectively. Peaks of flower litterfall for the four forests occurred during the transitional period between dry and rainy seasons, while peaks of fruit litterfall appeared either at the end of the rainy season at the two southern sites or in the dry season at the two northern sites. Leaf litterfall correlates significantly positively with preseason maximum temperature at the four sites, but significantly negatively with preseason precipitation at two southwest sites. By contrast, flower and fruit litterfall correlates significantly positively with preseason temperature and precipitation at only three and two sites. Moreover, leaf, flower, and fruit litterfall exhibits a 12-month cycle, which is consistent with the 12-month cycle of monthly temperature and precipitation. Flower and fruit litterfall displays also multiyear cycles between 18 and 48 months, however, it is inconsistent with the multiyear cycles of monthly temperature and precipitation. Our study highlights that temperature and precipitation are key factors affecting litterfall variations in different time scales in southern China.
... However wavelet coherency can overcome this limitation. Wavelet coherency measures the cross-correlation between two time series as a function of frequency this requires smoothing of both the cross-wavelet spectrum and the normalizing individual wavelet power spectra [16]: We can define the wavelet coherence between two time series using equation (19): ...
Article
Carbon markets are one of the measures that have been adopted by the Euro-pean Union Emissions Trading System(EU ETS) to address climate change. The Paris Agreement in December 2015 really highlighted the importance of the allocation of capital from the carbon market to achieve a global reduction in CO2 emissions[10]. Consequently, in-depth analysis of carbon market mechanisms could provide flexibility as to where and when greenhouse gas (GHG) emissions are reduced, and thus could reduce the costs of climate change mitigation, but also enable anticipate the behavior of market stakeholders concerning risk and expected return. Carbon prices exhibit non-stationary characteristics which makes them particularly hard to predict. In this paper, we introduce an hybrid forecasting model, incorporating multiscale analysis techniques, and other machine learning models to improve prediction accuracy of carbon prices. The co-movement between carbon prices and the COVID-19 pandemic is also investigated in the time-* Corresponding author. MRE EA 7491 (1 frequency domain using wavelet coherence. The proposed model for carbon price prediction outperforms other comparative models. The mean squared error(MSE), goodness of fit (R 2) and the Wilmott index of agreement of the proposed model are 0.0047, 0.9185 and 0.9801 respectively. The results on the co-movement show that there is a predominately strong positive co-movement of carbon prices with the COVID-19 pandemic.
... 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). ...
Article
Full-text available
The past decades have witnessed an increase in dissolved organic carbon (DOC) concentrations in the catchments of the Northern Hemisphere. Increasing terrestrial productivity and changing hydrology may be reasons for the increases in DOC concentration. The aim of this study is to investigate the impacts of increased terrestrial productivity and changed hydrology following climate change on DOC concentrations. We tested and quantified the effects of gross primary production (GPP), ecosystem respiration (RE) and discharge on DOC concentrations in boreal catchments over 3 years. As catchment characteristics can regulate the extent of rising DOC concentrations caused by the regional or global environmental changes, we selected four catchments with different sizes (small, medium and large) and landscapes (forest, mire and forest-mire mixed). We applied multiple models: Wavelet coherence analysis detected the delay-effects of terrestrial productivity and discharge on aquatic DOC variations of boreal catchments; thereafter, the distributed-lag linear models quantified the contributions of each factor on DOC variations. Our results showed that the combined impacts of terrestrial productivity and discharge explained 62% of aquatic DOC variations on average across all sites, whereas discharge, gross primary production (GPP) and RE accounted for 26%, 22% and 3%, respectively. The impact of GPP and discharge on DOC changes was directly related to catchment size: GPP dominated DOC fluctuations in small catchments (<1 km2 ), whereas discharge controlled DOC variations in big catchments (>1 km2 ). The direction of the relation between GPP and discharge on DOC varied. Increasing RE always made a positive contribution to DOC concentration. This study reveals that climate change-induced terrestrial greening and shifting hydrology change the DOC export from terrestrial to aquatic ecosystems. The work improves our mechanistic understanding of surface water DOC regulation in boreal catchments and confirms the importance of DOC fluxes in regulating ecosystem C budgets.
Article
Full-text available
En este artículo se presenta una concisa revisión de una de las herramientas más utilizadas en el proce-samiento de señales, el análisis espectral de wavelet mediante la transformada continua de wavelet para los casos uni-y bi-variados. Esta herramienta es sumamenteútil para analizar cualquier tipo de datos que no sean estacionarios, esto es, aquellos datos cuyas principales caractarísticas estadísticas (como la media o la varianza) cambian con el tiempo. El rango de aplicaciones de esta metodología es enorme, abarcando desde las ciencias experimentales (como la física o la ingeniería) hasta las ciencias sociales (como la economía o la arqueología). Sin embargo, y a pesar de que los ejemplos presentados en este artículo de revisión están relacionados con las ciencias ambientales, todos los conceptos teóricos así como los aspectos computacionales para usar esta técnica avanzada de procesamiento de señal son aplicables a cualquierárea de las ciencias e ingenierías. Adicionalmente, en este artículo de revisión se presentan varios programas computacionales libremente distribuidos (de tipo software libre o de fuentes abiertas) que realizan análisis espectral vía la transformada continua de wavelet. Palabras clave: wavelet, transformada continua de wavelet, espectro wavelet, correlación cruzada de wavelet, coherencia de wavelet. Abstract This article presents a short but concise review of one of the most used techniques in signal processing, the wavelet spectral analysis (WSA) via the continuous wavelet transform (CWT) for the uni-and bi-variate cases. This mathematical tool is very useful to analyse any kind of data that are not stationary, that is, data that their main statistical properties (such as the mean or the variance) can change with time. The range of applications of this methodology is enormous, ranging from experimental sciences (such as physics or engineering) to social sciences (such as economics or archaeology). However, and despite the fact that the examples presented in this review article are related to environmental sciences, all the theoretical concepts as well as the computational aspects to use this technique are applicable to any area of science or engineering. Additionally, this review article presents some freely distributed computer programs (of the free software or open source type) that perform spectral analysis via the continuous wavelet transform.
Preprint
Full-text available
In variable environments, phenotypic plasticity can increase fitness by providing tight environment-phenotype matching. However, adaptive plasticity is expected to evolve only when the future selective environment can be predicted based on the prevailing conditions. That is, the juvenile environment should be predictive of the adult environment (within-generation plasticity) or the parental environment should be predictive of the offspring environment (transgenerational plasticity). Here, we test links between environmental predictability and evolution of adaptive plasticity by combining time series analyses and a common garden experiment using temperature as a stressor in a temperate butterfly ( Melitaea cinxia ). Time series analyses revealed that across season fluctuations in temperature over 48 years is overall predictable. However, within the growing season, temperature fluctuations showed high heterogeneity across years with low autocorrelations and timing of temperature peaks were asynchronous. Most life-history traits showed strong within-generation plasticity for temperature and traits such as body size and growth rate broke the temperature-size rule. Evidence for transgenerational plasticity, however, was weak and detected for only two traits each in an adaptive and non-adaptive direction. We suggest that low predictability of temperature fluctuations within the growing season likely disfavours the evolution of adaptive transgenerational plasticity but instead favours strong within-generation plasticity.
Article
This paper probes deeper into the co-movement of Ghana's equity index and exchange rate with international equity markets and further determine whether these co-movements are driven by global uncertainties. Also, we sought to determine how the Ccovid-19 pandemic alters the dynamics of these relationships. We employ the wavelet technique to data from January 19, 2012 to March 1, 2021 to the split between pre-Covid-19 and Covid-19 periods. The results reveal that the dynamics of co-movement or interconnectedness of exchange rate and Ghana Stock Exchange composite index has evolved over time and across frequencies. Besides, the cone of influence, as shown by the wavelet spectrum, does not cover the entire data frequency which suggests that long-term forecast of exchange rate and equity index in Ghana beyond four years could be misleading since significant levels of interdependences are concentrated around the mid-team scales. In addition, we found evidence to support low-medium term lead-lag connections between exchange rate and Ghana Stock Exchange Composite Index in 2013 to 2014 and 2016. Further, the co-movement between exchange rate or Ghana Stock Exchange Composite Index and international equity markets show similarly weak association at all scales. A closer scan of the interdependencies among these variables are more intense during Covid-19 than during the pre-Covid-19 period. Finally, we observe a strong co-movement between the rise in Covid-19 cases and exchange rate at higher frequency scales where exchange rate lags Ghana's equity index and they are out-of-phase.
Article
Full-text available
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.
Article
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.
Article
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.
Article
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.
Article
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.