On the Use of Transfer Entropy to Investigate the Time Horizon of Causal Influences between Signals

Information flow among stocks, bonds, and convertible bonds

This study examines the information flow between convertible bonds (CBs) and other investment assets, such as stocks and bonds. In particular, we employ transfer entropy (TE) as a proxy for the causal effect between the two assets considering that one of the most widely used methods, Granger causality, requires strict assumptions. When adopting TE, we find that asymmetric information flow arising between assets depends on macroeconomic phases. The stock and bond markets affected the CB market prior to and during the global financial crisis, respectively. In the post-crisis period, we find no meaningful information exchange between CBs and other investment assets concerning their return series. However, we observe a significant cause-effect relationship between CBs and stocks in the rise-fall patterns of their price series. The findings suggest that the appearance of one-directional information flow depends on macroeconomic conditions and the level of data, for example, return series or price fluctuations. Accordingly, investors could exploit this pattern predictability in their portfolio management. In addition, policymakers must closely monitor the information flow among the three markets. When any two markets exchange information in a state of strong market integration, unbalanced regulation between them could lead to market distortions and regulatory arbitrage.

Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions

Transfer entropy (TE) has been used to identify and quantify interactions between physiological systems. Different methods exist to estimate TE, but there is no consensus about which one performs best in specific applications. In this study, five methods (linear, k-nearest neighbors, fixed-binning with ranking, kernel density estimation and adaptive partitioning) were compared. The comparison was made on three simulation models (linear, nonlinear and linear + nonlinear dynamics). From the simulations, it was found that the best method to quantify the different interactions was adaptive partitioning. This method was then applied on data from a polysomnography study, specifically on the ECG and the respiratory signals (nasal airflow and respiratory effort around the thorax). The hypothesis that the linear and nonlinear components of cardio-respiratory interactions during light and deep sleep change with the sleep stage, was tested. Significant differences, after performing surrogate analysis, indicate an increased TE during deep sleep. However, these differences were found to be dependent on the type of respiratory signal and sampling frequency. These results highlight the importance of selecting the appropriate signals, estimation method and surrogate analysis for the study of linear and nonlinear cardio-respiratory interactions.

A Refinement of Recurrence Analysis to Determine the Time Delay of Causality in Presence of External Perturbations

This article describes a refinement of recurrence analysis to determine the delay in the causal influence between a driver and a target, in the presence of additional perturbations affecting the time series of the response observable. The methodology is based on the definition of a new type of recurrence plots, the Conditional Joint Recurrence plot. The potential of the proposed approach resides in the great flexibility of recurrence plots themselves, which allows extending the technique to more than three quantities. Autoregressive time series, both linear and nonlinear, with different couplings and percentage of additive Gaussian noise have been investigated in detail, with and without outliers. The approach has also been applied to the case of synthetic periodic signals, representing realistic situations of synchronization experiments in thermonuclear fusion. The results obtained have been very positive; the proposed Conditional Joint Recurrence plots have always managed to identify the right interval of the causal influences and are very competitive with alternative techniques such as the Conditional Transfer Entropy.

Parallelism Strategies for Big Data Delayed Transfer Entropy Evaluation

Generated and collected data have been rising with the popularization of technologies such as Internet of Things, social media, and smartphone, leading big data term creation. One class of big data hidden information is causality. Among the tools to infer causal relationships, there is Delay Transfer Entropy (DTE); however, it has a high demanding processing power. Many approaches were proposed to overcome DTE performance issues such as GPU and FPGA implementations. Our study compared different parallel strategies to calculate DTE from big data series using a heterogeneous Beowulf cluster. Task Parallelism was significantly faster in comparison to Data Parallelism. With big data trend in sight, these results may enable bigger datasets analysis or better statistical evidence.

Noise Reduction Method of Underwater Acoustic Signals Based on Uniform Phase Empirical Mode Decomposition, Amplitude-Aware Permutation Entropy, and Pearson Correlation Coefficient

Noise reduction of underwater acoustic signals is of great significance in the fields of military and ocean exploration. Based on the adaptive decomposition characteristic of uniform phase empirical mode decomposition (UPEMD), a noise reduction method for underwater acoustic signals is proposed, which combines amplitude-aware permutation entropy (AAPE) and Pearson correlation coefficient (PCC). UPEMD is a recently proposed improved empirical mode decomposition (EMD) algorithm that alleviates the mode splitting and residual noise effects of EMD. AAPE is a tool to quantify the information content of nonlinear time series. Unlike permutation entropy (PE), AAPE can reflect the amplitude information on time series. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by UPEMD. The AAPE of each IMF is calculated. The modes are separated into high-frequency IMFs and low-frequency IMFs, and all low-frequency IMFs are determined as useful IMFs (UIMFs). Then, the PCC between the high-frequency IMF with the smallest AAPE and the original signal is calculated. If PCC is greater than the threshold, the IMF is also determined as a UIMF. Finally, all UIMFs are reconstructed and the denoised signal is obtained. Chaotic signals with different signal-to-noise ratios (SNRs) are used for denoising experiments. Compared with EMD and extreme-point symmetric mode decomposition (ESMD), the proposed method has higher SNR and smaller root mean square error (RMSE). The proposed method is applied to noise reduction of real underwater acoustic signals. The results show that the method can further eliminate noise and the chaotic attractors are smoother and clearer.