Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

Ordinal methods for a characterization of evolving functional brain networks

Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This-together with its conceptual simplicity and robustness against measurement noise-makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.

The Causality and Uncertainty of the COVID-19 Pandemic to Bursa Malaysia Financial Services Index's Constituents

Valued in hundreds of billions of Malaysian ringgit, the Bursa Malaysia Financial Services Index's constituents comprise several of the strongest performing financial constituents in Bursa Malaysia's Main Market. Although these constituents persistently reside mostly within the large market capitalization (cap), the existence of the individual constituent's causal influence or intensity relative to each other's performance during uncertain or even certain times is unknown. Thus, the key purpose of this paper is to identify and analyze the individual constituent's causal intensity, from early 2018 (pre-COVID-19) to the end of the year 2021 (post-COVID-19) using Granger causality and Schreiber transfer entropy. Furthermore, network science is used to measure and visualize the fluctuating causal degree of the source and the effected constituents. The results show that both the Granger causality and Schreiber transfer entropy networks detected patterns of increasing causality from pre- to post-COVID-19 but with differing causal intensities. Unexpectedly, both networks showed that the small- and mid-caps had high causal intensity during and after COVID-19. Using Bursa Malaysia's sub-sector for further analysis, the Insurance sub-sector rapidly increased in causality as the year progressed, making it one of the index's largest sources of causality. Even after removing large amounts of weak causal intensities, Schreiber transfer entropy was still able to detect higher amounts of causal sources from the Insurance sub-sector, whilst Granger causal sources declined rapidly post-COVID-19. The method of using directed temporal networks for the visualization of temporal causal sources is demonstrated to be a powerful approach that can aid in investment decision making.

Coherence Coefficient for Official Statistics

One of the quality requirements in official statistics is coherence of statistical information across domains, in time, in national accounts, and internally. However, no measure of its strength is used. The concept of coherence is also met in signal processing, wave physics, and time series. In the current article, the definition of the coherence coefficient for a weakly stationary time series is recalled and discussed. The coherence coefficient is a correlation coefficient between two indicators in time indexed by the same frequency components of their Fourier transforms and shows a degree of synchronicity between the time series for each frequency. The usage of this coefficient is illustrated through the coherence and Granger causality analysis of a collection of numerical economic and social statistical indicators. The coherence coefficient matrix-based non-metric multidimensional scaling for visualization of the time series in the frequency domain is a newly suggested method. The aim of this article is to propose the use of this coherence coefficient and its applications in official statistics.