Geophysical Applications of Partial Wavelet Coherence and Multiple Wavelet Coherence

Abstract

In this paper, the application of partial wavelet coherence (PWC) and multiple wavelet coherence (MWC) to geophysics is demonstrated. PWC is a technique similar to partial correlation that helps identify the resulting wavelet coherence (WTC) between two time series after eliminating the influence of their common dependence. MWC, akin to multiple correlation, is, however, useful in seeking the resulting WTC of multiple independent variables on a dependent one. The possible El Niño–Southern Oscillation–related impact of the large-scale atmospheric factors on tropical cyclone activity over the western North Pacific is used as an example. A software package for PWC and MWC has been developed. It also includes modified software that rectified the bias in the wavelet power spectrum and wavelet cross-spectrum. The package is available online (see http://www.cityu.edu.hk/gcacic/wavelet).

Examination of the International Causal Directions between Rates of Return on the Price Indices of the Selected Real Estate Markets in the CEE Region Using Wavelet Analysis

“…Furthermore, traditional Fourier analysis refers only to stationary time series, whereas the price indices considered in the current study, as well as a large number of macroeconomic data, exhibit nonstationarity. As a result, the research aim has been achieved using both the traditional methods of econometrics, such as the Granger causality tests, as well as wavelet analysis tools, commonly used, inter alia, in signal processing and geophysics applications [2,[33][34][35][36][37][38][39][40][41][42][43][44][45]. The toolbox contributed by AguiarConraria and Soares (ASToolbox) [8] has been used to perform simultaneous analysis of the considered time series in both the time and frequency domains, allowing to detect any potential structural changes dates on the considered investment markets.…”

“…1, gives an information on time changes in causality direction (phase lead of x(t) over y(t)), as well as an information on time changes in sign of co-movement between two analysed time series after controlling for third time series z(t) and is defined as [1,8,[44][45][46]:…”

Triadic Synchrony: Application of Multiple Wavelet Coherence to a Small Group Conversation

“…To handle this issue, as a first step, this study focused on triadic interaction, and tried to measure the overall synchrony from three individuals engaging a brainstorming task, a well-known small group task in an office meeting situation. As an index of triadic synchrony, I calculate a multiple wavelet coherence (MWC) [20] which seeks the resulting coherence of multiple independents on a dependent, like as multiple correlation. First, following [21], the continuous wavelet transform (CWT) is defined as:…”

“…Also, following [20] [21], the squared wavelet coherence (WTC), a tool for identifying possible relationships between two processes by searching frequency bands and time intervals during which they covariate, can be defined as:…”

“…Then, following [20], MWC, like multiple correlation that is capable of seeking the resulting coherence of multiple independents on a dependent, can be described as:…”