Entropy Analysis of Financial Time Series (original) (raw)

Applications of Entropy in Finance: A Review

Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.

Modeling the flow of information between financial time-series by an entropy-based approach

Annals of Operations Research, 2019

Recent literature has been documented that commodity prices have become more and more correlated with prices of financial assets. Hence, it would be crucial to understand how the amount of information contained in one time series (i.e. commodity prices) reflects on the other one (i.e. financial asset prices). Here, we address these issues by means of an entropybased approach. In particular, we define two new metrics, namely the Joined Entropy and the Mutual Information, to analyze and model how the information content is (mutually) exchanged between two time series under investigation. The experimental outcomes, applied on volatility indexes, oil and natural gas prices for the period 01/04/1999-01/02/2015, prove the effectiveness of the proposed method in modeling the information flows between the analyzed data. Keywords Information content • Modeling • Financial time-series • Volatility indexes • Crude oil spot prices • Entropy-based analysis JEL Classification C530 • C630 • G140 • Q470

Entropy Measures for Assessing Volatile Markets

Procedia Economics and Finance, 2015

The application of entropy in finance can be regarded as the extension of information entropy and probability theory. In this article we apply the concept of entropy for underlying financial markets to make a comparison between volatile markets. We consider in the first step Shannon entropy with different estimators, Tsallis entropy for different values of its parameter, Rényi entropy and finally the approximate entropy. We provide computational results for these entropies for weekly and monthly data in the case of four different stock indices.

Entropy: A new measure of stock market volatility?

Journal of Physics: Conference Series, 2012

When uncertainty dominates understanding stock market volatility is vital. There are a number of reasons for that. On one hand, substantial changes in volatility of financial market returns are capable of having significant negative effects on risk averse investors. In addition, such changes can also impact on consumption patterns, corporate capital investment decisions and macroeconomic variables. Arguably, volatility is one of the most important concepts in the whole finance theory. In the traditional approach this phenomenon has been addressed based on the concept of standard-deviation (or variance) from which all the famous ARCH type models -Autoregressive Conditional Heteroskedasticity Models-depart. In this context, volatility is often used to describe dispersion from an expected value, price or model. The variability of traded prices from their sample mean is only an example. Although as a measure of uncertainty and risk standard-deviation is very popular since it is simple and easy to calculate it has long been recognized that it is not fully satisfactory. The main reason for that lies in the fact that it is severely affected by extreme values. This may suggest that this is not a closed issue. Bearing on the above we might conclude that many other questions might arise while addressing this subject. One of outstanding importance, from which more sophisticated analysis can be carried out, is how to evaluate volatility, after all? If the standard-deviation has some drawbacks shall we still rely on it? Shall we look for an alternative measure? In searching for this shall we consider the insight of other domains of knowledge? In this paper we specifically address if the concept of entropy, originally developed in physics by Clausius in the XIX century, which can constitute an effective alternative. Basically, what we try to understand is, which are the potentialities of entropy compared to the standard deviation. But why entropy? The answer lies on the fact that there is already some research on the domain of Econophysics, which points out that as a measure of disorder, distance from equilibrium or even ignorance, entropy might present some advantages. However another question arises: since there is several measures of entropy which one since there are several measures of entropy, which one shall be used? As a starting point we discuss the potentialities of Shannon entropy and Tsallis entropy. The main difference between them is that both Renyi and Tsallis are adequate for anomalous systems while Shannon has revealed optimal for equilibrium systems.

Stock Market Volatility: An Approach Based on Tsallis Entropy

Arxiv preprint arXiv:0809.4570, 2008

One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known traditional techniques in the literature to measure stock market volatility, a central point in this debate that constitutes the actual scope of this paper is to compare this common approach in which we discuss such popular techniques as the standard deviation and an innovative methodology based on Econophysics. In our study, we use the concept of Tsallis entropy to capture the nature of volatility. More precisely, what we want to find out is if Tsallis entropy is able to detect volatility in stock market indexes and to compare its values with the ones obtained from the standard deviation. Also, we shall mention that one of the advantages of this new methodology is its ability to capture nonlinear dynamics. For our purpose, we shall basically focus on the behaviour of stock market indexes and consider the CAC 40, MIB 30, NIKKEI 225, PSI 20, IBEX 35, FTSE 100 and SP 500 for a comparative analysis between the approaches mentioned above.

Entropy-Based Financial Asset Pricing

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return – entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

Entropy Analysis of Real Time Series

2012

In the paper Entropy Analysis of Synthetic Time Series (Silber, M. & Vanlesberg, S.) properties of the entropy of the in- formation provided by synthetic series with different characteris- tics were demonstrated. In this opportunity, observed time series of precipitation on Mesopotamian and central region of Argentina were analyzed, with the following objectives: to verify the proper- ties shown in the cases described in the theoretical work mentioned above, the entropy of geographically related information with its variability and, in some way, to relate the empirical entropy (inde- pendent of the parameters of the theoretical probability distribution of the variable) with some of the variables included in the water bal- ance.

Entropy and predictability of stock market returns

Journal of Econometrics, 2002

We examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties. We compare our results with a number of traditional measures. The metric entropy is capable of detecting nonlinear dependence within the returns series, and is also capable of detecting nonlin-ear\a±nity" between the returns and their predictions obtained from various models thereby serving as a measure of out-of-sample goodness-of-¯t or model adequacy. Several models are investigated, including the linear and neural-network models as well as nonparametric and recursive unconditional mean models. We¯nd signi¯cant evidence of small nonlinear unconditional serial dependence within the returns series, but fragile evidence of superior conditional predictability (pro¯t opportunity) when using market-switching versus buy-and-hold strategies.

Estimating the Entropy of Binary Time Series: Methodology, Some Theory and a Simulation Study

Entropy, 2008

Partly motivated by entropy-estimation problems in neuroscience, we present a detailed and extensive comparison between some of the most popular and effective entropy estimation methods used in practice: The plug-in method, four different estimators based on the Lempel-Ziv (LZ) family of data compression algorithms, an estimator based on the Context-Tree Weighting (CTW) method, and the renewal entropy estimator.

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

Entropy

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respecti...