scholarly journals ANALYSIS OF THE TIME EVOLUTION OF NON-LINEAR FINANCIAL NETWORKS

2015 ◽  
Vol 3 (314) ◽  
Author(s):  
Paweł Fiedor
Keyword(s):  
Mutual Information ◽  
Stock Returns ◽  
Time Evolution ◽  
Correlation Coefficient ◽  
Spanning Trees ◽  
Stock Exchange ◽  
Financial Networks ◽  
Information Theoretic ◽  
Non Linear ◽  
Information Theoretic Measures

We treat financial markets as complex networks. It is commonplace to create a filtered graph (usually a Minimally Spanning Tree) based on an empirical correlation matrix. In our previous studies we have extended this standard methodology by exchanging Pearson’s correlation coefficient with information—theoretic measures of mutual information and mutual information rate, which allow for the inclusion of non-linear relationships. In this study we investigate the time evolution of financial networks, by applying a running window approach. Since information—theoretic measures are slow to converge, we base our analysis on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient, estimated by the Randomized Dependence Coefficient (RDC). It is defined in terms of canonical correlation analysis of random non-linear copula projections. On this basis we create Minimally Spanning Trees for each window moving along the studied time series, and analyse the time evolution of various network characteristics, and their market significance. We apply this procedure to a dataset describing logarithmic stock returns from Warsaw Stock Exchange for the years between 2006 and 2013, and comment on the findings, their applicability and significance.

scholarly journals Information-Theoretic Measures and Modeling Stock Market Volatility: A Comparative Approach

Risks ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 89
Author(s):  
Muhammad Sheraz ◽  
Imran Nasir
Keyword(s):  
Stock Market ◽  
Stock Returns ◽  
Stock Exchange ◽  
Approximate Entropy ◽  
Market Volatility ◽  
Comparative Approach ◽  
Stock Market Volatility ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Garch Modeling

The volatility analysis of stock returns data is paramount in financial studies. We investigate the dynamics of volatility and randomness of the Pakistan Stock Exchange (PSX-100) and obtain insights into the behavior of investors during and before the coronavirus disease (COVID-19 pandemic). The paper aims to present the volatility estimations and quantification of the randomness of PSX-100. The methodology includes two approaches: (i) the implementation of EGARCH, GJR-GARCH, and TGARCH models to estimate the volatilities; and (ii) analysis of randomness in volatilities series, return series, and PSX-100 closing prices for pre-pandemic and pandemic period by using Shannon’s, Tsallis, approximate and sample entropies. Volatility modeling suggests the existence of the leverage effect in both the underlying periods of study. The results obtained using GARCH modeling reveal that the stock market volatility has increased during the pandemic period. However, information-theoretic results based on Shannon and Tsallis entropies do not suggest notable variation in the estimated volatilities series and closing prices. We have examined regularity and randomness based on the approximate entropy and sample entropy. We have noticed both entropies are extremely sensitive to choices of the parameters.

scholarly journals Decomposing information into copying versus transformation

2020 ◽  
Vol 17 (162) ◽  
pp. 20190623 ◽  
Author(s):  
Artemy Kolchinsky ◽  
Bernat Corominas-Murtra
Keyword(s):  
Amino Acid ◽  
Mutual Information ◽  
Information Transfer ◽  
World Systems ◽  
Information Theoretic ◽  
Versus Transformation ◽  
Information Theoretic Measures ◽  
Functional Consequences ◽  
Standard Information ◽  
Minimal Work

In many real-world systems, information can be transmitted in two qualitatively different ways: by copying or by transformation . Copying occurs when messages are transmitted without modification, e.g. when an offspring receives an unaltered copy of a gene from its parent. Transformation occurs when messages are modified systematically during transmission, e.g. when mutational biases occur during genetic replication. Standard information-theoretic measures do not distinguish these two modes of information transfer, although they may reflect different mechanisms and have different functional consequences. Starting from a few simple axioms, we derive a decomposition of mutual information into the information transmitted by copying versus the information transmitted by transformation. We begin with a decomposition that applies when the source and destination of the channel have the same set of messages and a notion of message identity exists. We then generalize our decomposition to other kinds of channels, which can involve different source and destination sets and broader notions of similarity. In addition, we show that copy information can be interpreted as the minimal work needed by a physical copying process, which is relevant for understanding the physics of replication. We use the proposed decomposition to explore a model of amino acid substitution rates. Our results apply to any system in which the fidelity of copying, rather than simple predictability, is of critical relevance.

scholarly journals Predicting Extreme Daily Regime Shifts in Financial Time Series Exchange/Johannesburg Stock Exchange—All Share Index

2021 ◽  
Vol 9 (2) ◽  
pp. 18
Author(s):  
Katleho Makatjane ◽  
Ntebogang Moroke
Keyword(s):  
Time Series ◽  
Stock Returns ◽  
Linear Models ◽  
Stock Exchange ◽  
Financial Time Series ◽  
Moving Average ◽  
Autoregressive Integrated Moving Average ◽  
Financial Time ◽  
Johannesburg Stock Exchange ◽  
Non Linear

During the past decades, seasonal autoregressive integrated moving average (SARIMA) had become one of a prevalent linear models in time series and forecasting. Empirical research advocated that forecasting with non-linear models can be an encouraging alternative to traditional linear models. Linear models are often compared to non-linear models with mixed conclusions in terms of superiority in forecasting performance. Therefore, the aim of this study is to build an early warning system (EWS) model for extreme daily losses for financial stock markets. A logistic model tree (LMT) is used in collaboration with a seasonal autoregressive integrated moving average-Markov-Switching exponential generalised autoregressive conditional heteroscedasticity-generalised extreme value distribution (SARIMA-MS-EGARCH-GEVD) estimates. A time series of the study is a five-day financial time series exchange/Johannesburg stock exchange-all share index (FTSE/JSE-ALSI) for the period of 4 January 2010 to 31 July 2020. The study is set into a two-stage framework. Firstly, SARIMA model is fitted to stock returns in order to obtain independently and identically distributed (i.i.d) residuals and fit the MS(k)-EGARCH(p,q)-GEVD to i.i.d residuals; while, in the second stage, we set-up an EWS model. The results of the estimated MS(2)-EGARCH(1,1) -GEVD revealed that the conditional distribution of returns is highly volatile giving the expected duration to approximately 36 months and 4 days in regime one and 58 months and 2 days in regime two. We further found that any degree losses above 25% implies that there will be no further losses. Using the seven statistical loss functions, the estimated SARIMA(2,1,0)×(2,1,0)240−MS(2)−EGARCH(1,1)−GEVD proved to be the most appropriate model for predicting extreme regimes losses as it was ranked at 71%. Finally, the results of EWS model exhibit reasonably an overall performance of 98%, sensitivity of 79.89% and specificity of 98.40% respectively. The model further indicated a success classification rate of 89% and a prediction rate of 95%. This is a promising technique for EWS. The findings also confirmed 63% and 51% of extreme losses for both training sample and validation sample to be correctly classified. The findings of this study are useful for decision makers and financial sector for future use and planning. Furthermore, a base for future researchers for conducting studies on emerging markets, have been contributed. These results are also important to risk managers and and investors.

Link prediction in complex networks using information-theoretic measures

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Deepanshu Malhotra ◽  
Rinkaj Goyal
Keyword(s):  
Mutual Information ◽  
Complex Networks ◽  
Link Prediction ◽  
Structural Features ◽  
Engineering Systems ◽  
Form Complex ◽  
Information Theoretic ◽  
Information Measures ◽  
Prediction Algorithms ◽  
Information Theoretic Measures

Abstract Interconnections among real-world entities through explicit or implicit relationships form complex networks, such as social, economic and engineering systems. Recently, the studies based on such complex networks have provided a boost to our understanding of various events and processes ranging from biology to technology. Link prediction algorithms assist in predicting, analysing and deciphering more significant details about the networks and their future structures. In this study, we propose three different link prediction algorithms based on different structural features of the network combined with the information-theoretic analyses. The first two algorithms (variants) are developed for unweighted networks, while the third approach deals with the weighted ones. The proposed methods exhibit better and robust performances in the majority of cases, and at least comparable, if not better in other cases. This work is built upon the previously published mutual information-based approaches for link prediction; however, this study considers structural features of the network to augment mutual information measures and provides insights for finding hidden links in the network.

scholarly journals VOLATILITY INFERENCE AND RETURN DEPENDENCIES IN STOCHASTIC VOLATILITY MODELS

2019 ◽  
Vol 22 (03) ◽  
pp. 1950013
Author(s):  
OLIVER PFANTE ◽  
NILS BERTSCHINGER
Keyword(s):  
Mutual Information ◽  
Stock Returns ◽  
Stochastic Volatility ◽  
Wide Class ◽  
Factor Model ◽  
Stochastic Volatility Models ◽  
Information Theoretic ◽  
Random Dynamics ◽  
Fundamental Information ◽  
Volatility Models

Stochastic volatility models describe stock returns [Formula: see text] as driven by an unobserved process capturing the random dynamics of volatility [Formula: see text]. The present paper quantifies how much information about volatility [Formula: see text] and future stock returns can be inferred from past returns in stochastic volatility models in terms of Shannon’s mutual information. In particular, we show that across a wide class of stochastic volatility models, including a two-factor model, returns observed on the scale of seconds would be needed to obtain reliable volatility estimates. In addition, we prove that volatility forecasts beyond several weeks are essentially impossible for fundamental information theoretic reasons.

scholarly journals An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 79
Author(s):  
Ankush Aggarwal ◽  
Damiano Lombardi ◽  
Sanjay Pant
Keyword(s):  
Optimal Design ◽  
Mutual Information ◽  
Soft Tissues ◽  
Information Gain ◽  
Model Parameters ◽  
Conditional Mutual Information ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
New Framework ◽  
Biaxial Experiments

A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters. The proposed framework considers the information gain about the parameters from the experiment as the key criterion to be maximised, which can be directly used for optimal design. Information gain is computed through k-nearest neighbour algorithms applied to the joint samples of the parameters and measurements produced by the forward and observation models. For biaxial experiments, the results show that low angles have a relatively low information content compared to high angles. The results also show that a smaller number of angles with suitably chosen combinations can result in higher information gains when compared to a larger number of angles which are poorly combined. Finally, it is shown that the proposed framework is consistent with classical approaches, particularly D-optimal design.

A framework for causality under data assimilation

2020 ◽  
Author(s):  
Nachiketa Chakraborty ◽  
Peter Jan van Leeuwen ◽  
Michael de Caria ◽  
Manuel Pulido
Keyword(s):  
Causal Relation ◽  
Random Processes ◽  
Time Varying ◽  
Linear Dynamical Systems ◽  
Information Theoretic ◽  
Non Linear ◽  
Information Theoretic Measures ◽  
Non Gaussian ◽  
Causal Framework ◽  
Simple Systems

<p>Time varying processes in nature are often complex with non-linear and non-gaussian components. Complexity of environments and processes make it hard to disentangle different causal mechanisms which drives the observed time-series. It also makes it harder to make forecasts. The standard ways of studying causal relation in the geosciences which includes information theoretic measures of causation as well as predictive framework have deficiencies when applied to non-linear dynamical systems. Here we focus on investigating building a predictive causal framework that allows us to make predictions in simpler systems in a consistent way. We use a Bayesian framework to embed causal measures akin to mutual information from information theory to quantify relations between different random processes in this system. We examine causal relations in toy models and simple systems with a view to eventually applying to the interocean exchange problem in the Indian, the South Atlantic and the Southern Ocean. </p>

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

scholarly journals PENGARUH KURS, GROSS DOMESTIC PRODUCT DAN SOLVABILITAS TERHADAP RETURN SAHAM INVESTOR PADA PERUSAHAAN PERTAMBANGAN

2019 ◽  
Vol 8 (10) ◽  
pp. 6262
Author(s):  
Martina Carissa Dewi ◽  
Luh Gede Sri Artini
Keyword(s):  
Exchange Rate ◽  
Gross Domestic Product ◽  
Exchange Rates ◽  
Stock Returns ◽  
Stock Exchange ◽  
Sampling Technique ◽  
Domestic Product ◽  
Mining Company ◽  
Macroeconomic Factors ◽  
Regression Test

The level of return obtained by investors is influenced by microeconomic and macroeconomic factors. This study aims to obtain empirical evidence regarding the effect of exchange rates, Gross Domestic Product and solvency on stock returns. This research was conducted at the mining company in the coal sub-sector on the Indonesia Stock Exchange. All the coal mining sub-sector companies listed on the Stock Exchange for the period 2014-2017 used as the population. The method of determining the sample used is using a saturated sampling technique. Multiple linear regression test used as the data analysis on this research. Based on the results of the analysis of this study it was found that the exchange rate and GDP had a negative and significant effect on stock returns. The solvency proxied by DER has a positive and significant effect on stock returns. Keywords: Exchange Rate, Gross Domestic Product, Solvability and Return.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

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