wavScalogram: an R package with wavelet scalogram tools for time series analysis

TL;DR

The wavScalogram R package is presented, which contains methods based on wavelet scalograms for time series analysis related to two main wavelet tools: the windowed scalogram difference and the scale index.

Abstract

In this work we present the wavScalogram R package, which contains methods based on wavelet scalograms for time series analysis. These methods are related to two main wavelet tools: the windowed scalogram difference and the scale index. The windowed scalogram difference compares two time series, identifying if their scalograms follow similar patterns at different scales and times, and it is thus a useful complement to other comparison tools such as the squared wavelet coherence. On the other hand, the scale index provides a numerical estimation of the degree of non-periodicity of a time series and it is widely used in many scientific areas.

Figures (17)

• Figure 1: Real part (solid) and imaginary part (dashed) of Morlet, Paul and DoG wavelets for default parameter values, $\omega _0=6$ and $m=4,2$ respectively.
• Figure 2: Different constructions of an infinite signal from a finite length signal $\sin (t)$ with $t\in \left[-\pi ,\pi\right]$ (in red).
• Figure 3: Wavelet power spectra of signal, non corrected (a) and corrected (b) via parameter energy_density. The CoI is the shadowed region. This signal is the concatenation of two pure sinusoidal time series with the same amplitude and different periods. Note that even though both time series have the same amplitude, when the coefficients are not corrected, the magnitude of the wavelet power spectrum is biased in favour of large scales, while in the corrected version, this bias is not present.
• Figure 4: Original scalogram (a) and corrected scalogram representing an energy density measure (b), both relative to signal. As in Figure \ref{['fig:wps']}, it can be seen how the scalogram is biased in favour of large scales when the parameter energy_density is FALSE (plot (a)).
• Figure 5: Windowed scalogram (a) and windowed inner scalogram (b) of signal. The CoI is the shadowed region and, for the inner scalogram, the region where the scalogram cannot be computed is coloured in gray.

Theorems & Definitions (8)

• Remark 2.1: Fourier factor
• Remark 2.2: Energy density
• Remark 2.3: Border effects
• Remark 2.4: Cone of influence
• Remark 4.1: Normalization
• Remark 4.2: Near zero scalogram values
• Remark 5.1: No energy density
• Remark 5.2: Inner scalograms