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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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... For this analysis, we use the R-packages WaveletComp [37] that analyze the frequency structure of uni-and bivariate time series using the Morlet mother wavelet [33,35] ...
... This leads to a continuous complex-valued wavelet transform that can be separated into its real and imaginary parts, providing information on both local amplitude and instantaneous phase of any periodic process across time, a prerequisite for investigating multiple time series coherence [37]. ...
... The concepts of cross-wavelet analysis provide a tool for (i) comparing the frequency of twotime series, (ii) concluding the series' synchronicity at specific frequencies and across certain ranges of time [37]. Its modulus can be interpreted as cross-wavelet power. ...
Dengue transmission poses significant challenges for public health authorities worldwide due to its susceptibility to various factors, including environmental and climate variability, affecting its incidence and geographic spread. This study focuses on Costa Rica, a country characterized by diverse microclimates nearby, where dengue has been endemic since its introduction in 1993. Using wavelet coherence and clustering analysis, we performed a time-series analysis to uncover the intricate connections between climate, local environmental factors, and dengue occurrences. The findings indicate that multiannual dengue frequency (3 yr) is correlated with the Oceanic Niño Index and the Tropical North Atlantic Index. This association is particularly prominent in cantons located along the North and South Pacific Coast, as well as in the Central cantons of the country. Furthermore, the time series of these climate indices exhibit a leading phase of approximately nine months ahead of dengue cases. Additionally, the clustering analysis uncovers non-contiguous groups of cantons that exhibit similar correlation patterns, irrespective of their proximity or adjacency. This highlights the significance of climate factors in influencing dengue dynamics across diverse regions, regardless of spatial closeness or distance between them. On the other hand, the annual dengue frequency was correlated with local environmental indices. A persistent correlation between dengue cases and local environmental variables is observed over time in the North Pacific and the Central Region of the country's Northwest, with environmental factors leading by less than three months. These findings contribute to understanding dengue transmission's spatial and temporal dynamics in Costa Rica, highlighting the importance of climate and local environmental factors in dengue surveillance and control efforts.
... The difference in phase between two time-series data depicts an in-phase oscillation pattern of two time-series data if they are matched with each other; in contrast, the difference in phase depicts an out-of-phase pattern if the two time-series data do not match (Grinsted et al., 2004). The lagging or the leading tendencies of the variables are indicated through the arrows (Schmidbauer and Roesch, 2018). The coherence between the variables was evaluated at the p-value of 0.05 and was incorporated in the cone of influence (Pal and Devara, 2012). ...
... The coherence between the variables was evaluated at the p-value of 0.05 and was incorporated in the cone of influence (Pal and Devara, 2012). The entire process of wavelet analysis and its graphical expression was performed in RStudio using the WaveletComp package (Schmidbauer and Roesch, 2018). To detect the presence or absence of multicollinearity among climatic variables, the variance inflation factor (VIF) was obtained in RStudio using the faraway package (Faraway, 2022). ...
... The maximum CWP level was observed after 2010 and in the period segment of the 11th to the 12th month period in a discrete manner. The arrows in the segments toward the right (fifth to the seventh month period) and top-right (ninth to the 12th month period) directions indicate the in-phase cyclicity of evapotranspiration and NDVI (Schmidbauer and Roesch, 2018;Liu et al., 2023). In the case of the ninth to the 12th month period, the segment was associated with the situation when the mean NDVI was leading and evapotranspiration was lagging. ...
An arid climate is a unique condition that has a significant impact on the growth of
crops and natural vegetation. The normalized difference vegetation index (NDVI) is
a crucial remotely sensed measurement of greenness due to its strong correlation
with crop and vegetation growth and productivity. In the present study, the
spatiotemporal dynamics of NDVI were analyzed from 2000 to 2021 in the
segment of the arid western plain zone of Rajasthan, India. NDVI time-series
data, as well as data related to climatic factors, viz., precipitation, soil moisture,
evapotranspiration, and 2-m air temperature, were collected from Giovanni, the
Goddard Earth Science dataset. The Mann–Kendall (MK) trend test and Sen’s slope
depicted the long-term continuous time–frequency trend, while Karl Pearson’s
correlation analysis depicted the significant relationship between all the factors
except 2-m air temperature. The seasonal and mean monthly results of all the
factors except 2-m air temperature showed considerable coherence with NDVI.
The multiscale time–frequency decomposition or wavelet analysis depicted the
fifth to the seventh month and the ninth to the 15th month of the cycle, showing
the significance of the cropping pattern and the natural vegetation growth cycle.
The cross-wavelet analysis further depicted important coherence, leading, and
lagging phases among climatic factors and NDVI. Our research provided
significant insights into the long-term variability and coherence of various
climatic factors with NDVI that are applicable on regional and global scales.
... The overall data processing and analysis was done in R environment. The wavelet analysis was done using WaveletComp package [11]. The time series was detrended before the application of wavelet transformation. ...
The characterization of the cyclical nature of semiconductor industry is a complex endeavor because of the presence of many interacting transient dynamics inherent in the industry's ecosystem. In this paper we present a methodology that addresses some of the issues, particularly the non-stationarity of the time series associated with the semiconductor industry. We use singular spectrum analysis to de-noise data before identifying the dominant pattern of the semiconductor stock market using singular value decomposition. By using continuous wavelet transformation and cross-wavelet coherence relation, the nexus between the dominant pattern of the stock market and the industrial production index of semiconductor is established. Using a bootstrap resampling method, statistically significant frequencies that characterize the cyclical nature of the semiconductor industry are identified.
... We therefore calculated a Fourier decomposition of each timeseries in addition to a time-averaged wavelet decomposition of each timeseries, meaning we obtained two semi-redundant frequency representations of our data. However, because the wavelet transform uses a differently-shaped "mother wavelet," and because it is not perfectly information-preserving when averaged across time, it will have some differences (Schmidbauer & Roesch, 2018;Torrence & Compo, 1998). We found that some information loss was advantageous because it reduced noise that otherwise obscured patterns in the data. ...
River flows change on timescales ranging from minutes to millennia. These vibrations in flow are tuned by diverse factors globally, for example, by dams suppressing multi‐day variability or vegetation attenuating flood peaks in some ecosystems. The relative importance of the physical, biological, and human factors influencing flow is an active area of research, as is the related question of finding a common language for describing overall flow regime. Here, we addressed both topics using a daily river discharge data set for over 3,000 stations across the globe from 1988 to 2016. We first studied similarities between common flow regime quantification methods, including traditional flow metrics, wavelets, and Fourier analysis. Across all these methods, the flow data showed low‐dimensional structure (i.e., simple and consistent patterns), suggesting that fundamental mechanisms are constraining flow regime. One such pattern was that day‐to‐day variability was negatively correlated with year‐to‐year variability. Additionally, the low‐dimensional structure in river flow data correlated closely with only a small number of catchment characteristics, including catchment area, precipitation, and temperature—but notably not biome, dam surface area, or number of dams. We discuss these findings in a framework intended to be accessible to the many communities engaged in river research and management, while stressing the importance of letting structure in data guide both mechanistic inference and interdisciplinary discussion.
Arid and semi-arid regions are vulnerable to natural disturbances and particularly, to anthropogenic climate change. In these regions, water resources are scarce, and groundwater is commonly the main source of water for municipal supply, agricultural, and industrial purposes. Groundwater overexploitation is a common issue for these regions, where overextraction, climate variability, and recharge are responsible for groundwater storage evolution. This study aims to find teleconnections through wavelet analysis between inter-annual rates of change in storage, obtained from geostatistical groundwater modeling, and climate variability. Continuous wavelet transform, cross-wavelet analysis, and wavelet coherence were used to analyze and characterize non-stationary patterns of variability of precipitation (PP), standardized precipitation index (SPI), minimum (Min_Temp) and maximum temperature (Max_Temp), Enhanced Vegetation Index (EVI), the Oceanic Niño Index (ONI), the Pacific-North American pattern (PNA), the Caribbean Index (CAR), and groundwater change in storage (ΔGS) semestral time series. The results suggest significant influences of the indices on ΔGS, PP, Min_Temp, and EVI. PNA manifested an important influence in short periods (2–4 years) in all aquifers, ONI showed influence mainly over long periods (8–16 years), and CAR had influence in periods of high hurricane activities. In addition, under extreme climatic conditions (El Niño or La Niña) the higher/lower water demand increase their influence on groundwater level response creating an indirect link between climate indices and ΔGS. This research can serve as a good indicator of the climate variations behavior and can provide information to understand the regional climate effects of the ENSO phenomenon in overexploited aquifers.
Graphical abstract
Since the drought is a significant issue in India, therefore, the scientists should pay close attention in order to manage it. Purulia District experienced the drought on numerous occasions in the past ten years, but the accurate and definite conclusions have not arrived yet. Hence, the Standardized Precipitation Index (SPI) for the 34 years (1979–2014) was utilised in this research together with the change point to evaluate the annual and seasonal drought in the Purulia District. Theil Sen's slope and the Mann-Kendal (MK) test were both employed to determine the trend and its’ magnitude. A trend-free pre-whitening technique was used to remove the influence of lag-1 correlation data from the series. The 1988-89 was marked as the best probable single change (shift) point in the time series of SPI. By calculating the percentage deviation from the SPI's mean trend, the magnitude of the change was calculated. The percentage change of Sen's slope and MK test was high (+ve) at the eastern parts of Purulia, whereas it was observed as the smallest at the southern parts of the region. Thus, it could be concluded that the drought had begun to spread to the study region's eastern sections after the change point. As Purulia is dependent on agricultural crop production, this research would significantly contribute to agricultural planning following the local level management of crop water and rain-water harvesting. Therefore, this research is extremely important for the drought risk management on a regional scale.
This study investigates the temporal variability of the northeast monsoon rainfall (NEMR) in India and its relationship with El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) using wavelet analysis. The results show that NEMR is highly variable, with a coefficient of variation of about 25%, which is due to its dependence on dynamic systems with a wide range of spatial and temporal scales. The temporal variability of NEMR is at different time scales ranging from intra-annual to interannual to decadal time scales. The large-scale circulation features, ENSO and IOD, also exhibit variability at different time scales. El Niño events have a typical frequency range of 2 to 7 years, with a prolonged impact that can last for several months, spreading across the globe. Wavelet transforms of SOI and Nino 3.4 have revealed variability at the time scale of 2–8 years, which is in line with the observed ENSO cycle. The wavelet transform of DMI displays significant variability in short time scales, typically less than 2–4 years. The study also finds a strong negative relationship between NEMR and SOI, recorded in September, especially over Tamil Nadu, Kerala, and Coastal Andhra Pradesh during the periods 1900–1920 and 1980–2000. This correlation is strong at time scales of 2–4 years and 4–8 years during the periods 1880–1920, possibly related to the ENSO cycle and the oscillation of anomalous SST over the Indian Ocean. The study highlights the need for further studies to understand the physical processes that contribute to the observed variability in El Niño and other ocean–atmosphere interactions.
This study investigates the seasonality pattern and association between meteorological factors and particulate matter (PM10) concentration, and influenza incidence in Bangkok, Thailand. We analyze monthly averaged temperature, relative humidity, precipitation, PM10 concentrations, and influenza cases collected from 2003 to 2019 using wavelet analysis and a generalized additive model (GAM). The wavelet transforms analysis shows the periodic patterns of influenza with distinct periods of 0.5 years prior to the influenza pandemic in 2009 and 0.5 and 1 year following the pandemic, demonstrating an important shift after the 2009 pandemic. The result also reveals a significant coherence between climate factors, PM10, and influenza incidence. By using the maximum lag time obtained from the wavelet analysis, our GAM model shows the linear relationships between PM10, relative humidity, precipitation, and influenza incidence, whereas temperature exhibits a nonlinear relationship with influenza cases. These findings contribute to a better understanding of the temporal dynamics of influenza seasonality driven by climate factors and PM10 during the past 17 years. This knowledge would be useful for planning clinical resources and supporting public health under the climate situation in Thailand.
Previous research has extensively explored the direct impact of renewable energy on carbon emissions. This paper investigates three points against this backdrop. The first point is whether renewable energy operates as a moderated, moderating, or mediating variable in influencing the direct or indirect effects of growth on carbon emissions. The second point is which models should be used to estimate these three functions of renewable energy. The third point is whether these three functions should be estimated using aggregate or disaggregate data. The study draws two major findings. First, the three functions of renewable energy in influencing the impact of growth on carbon emissions should be investigated using moderated mediation models in which nonrenewable energy serves as a moderating or mediating variable and financial development serves as a moderating variable. Second, these models should be estimated using both aggregate and disaggregate proxies for renewable energy, economic growth, and financial development. Based on its empirical findings, the study presents pertinent policy suggestions for assessing the three roles of renewable energy.
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.