scholarly journals On Geometry of Information Flow for Causal Inference

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 396
Author(s):  
Sudam Surasinghe ◽  
Erik M. Bollt
Keyword(s):  
Causal Inference ◽  
Information Flow ◽  
Geometric Interpretation ◽  
Rate Function ◽  
Transfer Entropy ◽  
Complex Nature ◽  
Outcome Space ◽  
Underlying Manifold ◽  
Effective Dimensionality ◽  
Synthetic Models

Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine learning experts, and scientists from many other fields. This paper takes the perspective of information flow, which includes the Nobel prize winning work on Granger-causality, and the recently highly popular transfer entropy, these being probabilistic in nature. Our main contribution will be to develop analysis tools that will allow a geometric interpretation of information flow as a causal inference indicated by positive transfer entropy. We will describe the effective dimensionality of an underlying manifold as projected into the outcome space that summarizes information flow. Therefore, contrasting the probabilistic and geometric perspectives, we will introduce a new measure of causal inference based on the fractal correlation dimension conditionally applied to competing explanations of future forecasts, which we will write G e o C y → x . This avoids some of the boundedness issues that we show exist for the transfer entropy, T y → x . We will highlight our discussions with data developed from synthetic models of successively more complex nature: these include the Hénon map example, and finally a real physiological example relating breathing and heart rate function.

scholarly journals Applying transfer entropy approach to investigate the information flow among ASEAN stock markets

2020 ◽  
Vol 4 (1) ◽  
pp. First
Author(s):  
Tran Thi Tuan Anh
Keyword(s):  
Information Flow ◽  
Stock Markets ◽  
Investment Strategy ◽  
The Philippines ◽  
Transfer Entropy ◽  
The Other ◽  
Information Flows ◽  
Research Results ◽  
Region Data ◽  
Asean Countries

This paper uses transfer entropy to measure and identify the information flows between stock markets in the ASEAN region. Data on daily closing stock indices, including Vietnam, the Philippines, Malaysia, Indonesia, Thailand, and Singapore, are collected for the period from March 2012 to October 2019 to calculate these transfer entropies. The research results of this article can be considered in two aspects: one is, how information flow originating from one market will be accepted by other markets and secondly, information flow that markets receive. From the perspective of incoming transfer entropy, Vietnam is the country most affected by information from the other ASEAN markets while Indonesia and Malaysia are the least affected. In terms of outgoing entropy, Thailand is the largest source of information flow to the ASEAN markets. Malaysia and the Philippines are the two countries that receive minor information impact from other countries. The research also reveals that the Singapore stock market is rather separate from the other ASEAN countries. The research results also imply that, for investors and policymakers, defining the information flows among ASEAN stock markets can help to predict market movements, thereby developing a suitable investment strategy or establishing appropriate management policies.

scholarly journals Quantification of Information Exchange in Idealized and Climate System Applications

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1094
Author(s):  
Praveen Kumar Pothapakula ◽  
Cristina Primo ◽  
Bodo Ahrens
Keyword(s):  
Nonlinear Systems ◽  
Sample Size ◽  
Information Flow ◽  
Air Temperature ◽  
Information Exchange ◽  
Nearest Neighbor ◽  
Climate System ◽  
Transfer Entropy ◽  
K Nearest Neighbor ◽  
Lorenz 96

Often in climate system studies, linear and symmetric statistical measures are applied to quantify interactions among subsystems or variables. However, they do not allow identification of the driving and responding subsystems. Therefore, in this study, we aimed to apply asymmetric measures from information theory: the axiomatically proposed transfer entropy and the first principle-based information flow to detect and quantify climate interactions. As their estimations are challenging, we initially tested nonparametric estimators like transfer entropy (TE)-binning, TE-kernel, and TE k-nearest neighbor and parametric estimators like TE-linear and information flow (IF)-linear with idealized two-dimensional test cases along with their sensitivity on sample size. Thereafter, we experimentally applied these methods to the Lorenz-96 model and to two real climate phenomena, i.e., (1) the Indo-Pacific Ocean coupling and (2) North Atlantic Oscillation (NAO)–European air temperature coupling. As expected, the linear estimators work for linear systems but fail for strongly nonlinear systems. The TE-kernel and TE k-nearest neighbor estimators are reliable for linear and nonlinear systems. Nevertheless, the nonparametric methods are sensitive to parameter selection and sample size. Thus, this work proposes a composite use of the TE-kernel and TE k-nearest neighbor estimators along with parameter testing for consistent results. The revealed information exchange in Lorenz-96 is dominated by the slow subsystem component. For real climate phenomena, expected bidirectional information exchange between the Indian and Pacific SSTs was detected. Furthermore, expected information exchange from NAO to European air temperature was detected, but also unexpected reversal information exchange. The latter might hint to a hidden process driving both the NAO and European temperatures. Hence, the limitations, availability of time series length and the system at hand must be taken into account before drawing any conclusions from TE and IF-linear estimations.

scholarly journals Quantifying the Information Flow between Ghana Stock Market Index and Its Constituents Using Transfer Entropy

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Prince Mensah Osei ◽  
Anokye M. Adam
Keyword(s):  
Stock Market ◽  
Information Flow ◽  
Information Exchange ◽  
Oil And Gas ◽  
Transfer Entropy ◽  
Stock Market Index ◽  
Insurance Sector ◽  
Market Index ◽  
The Individual ◽  
Effective Transfer

We quantify the strength and the directionality of information transfer between the Ghana stock market index and its component stocks as well as observe the same among the individual stocks on the market using transfer entropy. The information flow between the market index and its components and among individual stocks is measured by the effective transfer entropy of the daily logarithm returns generated from the daily market index and stock prices of 32 stocks ranging from 2nd January 2009 to 16th February 2018. We find a bidirectional and unidirectional flow of information between the GSE index and its component stocks, and the stocks dominate the information exchange. Among the individual stocks, SCB is the most active stock in the information exchange as it is the stock that receives the highest amount of information, but the most informative source is EGL (an insurance company) that has the highest net information outflow while the most information sink is PBC that has the highest net information inflow. We further categorize the stocks into 9 stock market sectors and find the insurance sector to be the largest source of information which confirms our earlier findings. Surprisingly, the oil and gas sector is the information sink. Our results confirm the fact that other sectors including oil and gas mitigate their risk exposures through insurance companies and are always expectant of information originating from the insurance sector in relation to regulatory compliance issues. It is our firm conviction that this study would allow stakeholders of the market to make informed buy, sell, or hold decisions.

DATA DISCRETIZATION FOR THE TRANSFER ENTROPY IN FINANCIAL MARKET

2013 ◽  
Vol 12 (04) ◽  
pp. 1350019 ◽  
Author(s):  
XUEJIAO WANG ◽  
PENGJIAN SHANG ◽  
JINGJING HUANG ◽  
GUOCHEN FENG
Keyword(s):  
Financial Market ◽  
Information Flow ◽  
Coarse Graining ◽  
Transfer Entropy ◽  
Linear Modeling ◽  
Information Theoretic ◽  
Model Free ◽  
Temporal Correlations ◽  
Data Discretization ◽  
Flow Of Information

Recently, an information theoretic inspired concept of transfer entropy has been introduced by Schreiber. It aims to quantify in a nonparametric and explicitly nonsymmetric way the flow of information between two time series. This model-free based on Shannon entropy approach in principle allows us to detect statistical dependencies of all types, i.e., linear and nonlinear temporal correlations. However, we always analyze the transfer entropy based on the data, which is discretized into three partitions by some coarse graining. Naturally, we are interested in investigating the effect of the data discretization of the two series on the transfer entropy. In our paper, we analyze the results based on the data which are generated by the linear modeling and the ARFIMA modeling, as well as the dataset consists of seven indices during the period 1992–2002. The results show that the higher the degree of data discretization get, the larger the value of the transfer entropy will be, besides, the direction of the information flow is unchanged along with the degree of data discretization.

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