We propose a modified time lag random matrix theory in order to study time lag cross-correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross-correlations in the absolute values of returns that quantify risk, and find that they decay much more slowly than cross-correlations between the returns. The magnitude of the cross-correlations constitute "bad news" for international investment managers who may believe that risk is reduced by diversifying across countries. We find that when a market shock is transmitted around the world, the risk decays very slowly. We explain these time lag cross-correlations by introducing a global factor model (GFM) in which all index returns fluctuate in response to a single global factor. For each pair of individual time series of returns, the cross-correlations between returns (or magnitudes) can be modeled with the auto-correlations of the global factor returns (or magnitudes). We estimate the global factor using principal component analysis, which minimizes the variance of the residuals after removing the global trend. Using random matrix theory, a significant fraction of the world index cross-correlations can be explained by the global factor, which supports the utility of the GFM. We demonstrate applications of the GFM in forecasting risks at the world level, and in finding uncorrelated individual indices. We find 10 indices are practically uncorrelated with the global factor and with the remainder of the world indices, which is relevant information for world managers in reducing their portfolio risk. Finally, we argue that this general method can be applied to a wide range of phenomena in which time series are measured, ranging from seismology and physiology to atmospheric geophysics.
Using transfer entropy, we observed the strength and direction of information flow between stock indices. We uncovered that the biggest source of information flow is America. In contrast, the Asia/Pacific region the biggest is receives the most information. According to the minimum spanning tree, the GSPC is located at the focal point of the information source for world stock markets.
We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A change in market state is identified as a change in the first PC coefficients. Some indices do not show significant change of PCs in market state during crises. The indices exposed to the invested capitals in the stock markets are at the minimum level of risk. Using the first two…
The aim of this paper is to compare statistical properties of stock price indices in periods of booms with those in periods of stagnations. We use the daily data of the four stock price indices in the major stock markets in the world: (i) the Nikkei 225 index (Nikkei 225) from January 4, 1975 to August 18, 2004, of (ii) the Dow Jones Industrial Average (DJIA) from January 2, 1946 to August 18, 2004, of (iii) Standard and Poor's 500 index (SP500) from November 22, 1982 to August 18, 2004, and of (iii) the Financial Times Stock Exchange 100 index (FT 100) from April 2, 1984 to August 18, 2004. W…
The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such auto-correlations. Their characteristic time-scale proves to be smaller (less than $25$ trading days) than what was previously believed. It is also found that this …
Stock market indices are one of the most investigated complex systems in econophysics. Here we extend the existing literature on stock markets in connection with nonextensive statistical mechanics. We explore the nonextensivity of price volatilities for 34 major stock market indices between 2010 and 2019. We discover that stock markets follow nonextensive statistics regarding equilibrium, relaxation and sensitivity. We find nonextensive behavior in stock markets for developed countries, but not for developing countries. Distances between nonextensive triplets suggest that some stock markets mi…
This study examined how the correlation and network structure of 30 global indices and 145 local Korean indices belonging to the KOSPI 200 have changed during the 13-year period, 2000-2012. The correlations among the indices were calculated. The results showed that although the average correlations of the global indices increased with time, the local indices showed a decreasing trend except for drastic changes during crises. The average correlation of the local indices exceeded the global indices during the crises from 2000-2002, implying a strong correlation structure among the local indices …
We demonstrate that the gain/loss asymmetry observed for stock indices vanishes if the temporal dependence structure is destroyed by scrambling the time series. We also show that an artificial index constructed by a simple average of a number of individual stocks display gain/loss asymmetry - this allows us to explicitly analyze the dependence between the index constituents. We consider mutual information and correlation based measures and show that the stock returns indeed have a higher degree of dependence in times of market downturns than upturns.
How an investor invests in the market is largely influenced by the market efficiency because if a market is efficient, it is extremely difficult to make excessive returns because in an efficient market there will be no undervalued securities i.e. securities whose value is less than its assumed intrinsic value, which offer returns that are higher than the deserved expected returns, given their risk. However, there is a possibility of making excessive returns if the market is not efficient. This article analyses the five popular stock indices of BSE. This would not only test the efficiency of th…
We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [λ_, λ+], where λ_- and λ_+ are the lower and the upper bounds of the eigenvalues of rand…
Using the tools developed for statistical physics, we simultaneously analyze statistical properties of the Jakarta and Kuala Lumpur Stock Exchange indices. In spite of the small number of data used in the analysis, the result shows the universal behavior of complex systems previously found in the leading stock indices. We also analyze their features before and after the financial crisis. We found that after the crisis both stocks do not show a same statistical behavior. The impact of currency controls is observed in the distribution of index returns.
The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph. A universal allometric scaling law is uncovered in the minimal spanning trees, whose scaling exponent is independent of the stock market and the length of the stock index. In contrast, the maximal…
We consider returns of two Korean stock market indices, KOSPI and KOSDAQ index. Central parts of the probability distribution function of returns are well fitted by the Lorentzian distribution function. However, tail parts of the probability distribution function follow a power law behavior well. We found that the probability distribution function of returns for both KOSPI and KOSDAQ, is outside the Lévy stable distribution.
The statistical properties of the bid-ask spread of a frequently traded Chinese stock listed on the Shenzhen Stock Exchange are investigated using the limit-order book data. Three different definitions of spread are considered based on the time right before transactions, the time whenever the highest buying price or the lowest selling price changes, and a fixed time interval. The results are qualitatively similar no matter linear prices or logarithmic prices are used. The average spread exhibits evident intraday patterns consisting of a big L-shape in morning transactions and a small L-shape i…
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about…
We investigate sets of financial non-redundant and nonsynchronously recorded time series. The sets are composed by a number of stock market indices located all over the world in five continents. By properly selecting the time horizon of returns and by using a reference currency we find a meaningful taxonomy. The detection of such a taxonomy proves that interpretable information can be stored in a set of nonsynchronously recorded time series.
Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell) or three options. However, herding effects of competing stocks and the collective dynamics of a whole market may escape our reach in the simplest models. Here I study a q-spin Potts model version of a simple Ising market model to represent the dynamics of a stock market index in a spin model. As a result, a self-organized gain-loss asymmetry in the time ser…
We use Random Matrix Theory (RMT) and information theory to analyze the correlations and flow of information between 64,939 news from The New York Times and 40 world financial indices during 10 months along the period 2015-2016. The set of news was quantified and transformed into daily polarity time series using tools from sentiment analysis. Results from RMT shows that a common factor lead the world indices and news, and even share the same dynamics. Furthermore, the global correlation structure has found preserved when adding white noise, which indicate that correlations are not due to sampl…
Among other macroeconomic indicators, the monthly release of U.S. unemployment rate figures in the Employment Situation report by the U.S. Bureau of Labour Statistics gets a lot of media attention and strongly affects the stock markets. I investigate whether a profitable investment strategy can be constructed by predicting the likely changes in U.S. unemployment before the official news release using Google query volumes for related search terms. I find that massive new data sources of human interaction with the Internet not only improves U.S. unemployment rate predictability, but can also enh…
In this paper, we model the impact of oil price volatility on Tehranstock and industry indices in two periods of international sanctions and post-sanction. To analyse the purpose of study, we use Feed-forward neural net-works. The period of study is from 2008 to 2018 that is split in two periods during international energy sanction and post-sanction. The results show that Feed-forward neural networks perform well in predicting stock market and industry, which means oil price volatility has a significant impact on stock and industry market indices. During post-sanction and global financial cris…
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition method. We investigate the influences of trading behaviors on the price impact by comparing a closed national market (A-shares) with an international market (B-shares), individuals and institutions, partially filled and filled trades, buyer-initiated and seller-initiated trades, a…
We develop a novel temporal complex network approach to quantify the US county level spread dynamics of COVID-19. The objective is to study the effects of the local spread dynamics, COVID-19 cases and death, and Google search activities on the US stock market. We use both conventional econometric and Machine Learning (ML) models. The results suggest that COVID-19 cases and deaths, its local spread, and Google searches have impacts on abnormal stock prices between January 2020 to May 2020. In addition, incorporating information about local spread significantly improves the performance of foreca…
A classification of companies into sectors of the economy is important for macroeconomic analysis and for investments into the sector-specific financial indices and exchange traded funds (ETFs). Major industrial classification systems and financial indices have historically been based on expert opinion and developed manually. Here we show how unsupervised machine learning can provide a more objective and comprehensive broad-level sector decomposition of stocks. An emergent low-dimensional structure in the space of historical stock price returns automatically identifies "canonical sectors" in t…
Selecting stock portfolios and assessing their relative volatility risk compared to the market as a whole, market indices, or other portfolios is of great importance to professional fund managers and individual investors alike. Our research uses the cross-sectional intrinsic entropy (CSIE) model to estimate the cross-sectional volatility of the stock groups that can be considered together as portfolio constituents. In our study, we benchmark portfolio volatility risks against the volatility of the entire market provided by the CSIE and the volatility of market indices computed using longitudin…
This paper investigates the presence of long memory in corporate bond and stock indices of six European Union countries from July 1998 to February 2015. We compute the Hurst exponent by means of the DFA method and using a sliding window in order to measure long range dependence. We detect that Hurst exponents behave differently in the stock and bond markets, being smoother in the stock indices than in the bond indices. We verify that the level of informational efficiency is time-varying. Moreover we find an asymmetric impact of the 2008 financial crisis in the fixed income and the stock market…
Recently, a stock price model is proposed by A. Mahata et al. [Physica A, 574, 126008 (2021)] to understand the effect of COVID-19 on stock market. It describes V- and L-shaped recovery of the stocks and indices, but fails to simulate the U- and Swoosh-shaped recovery that arises due to sharp crisis and prolong drop followed by quick recovery (U-shaped) or slow recovery for longer period (Swoosh-shaped recovery). We propose a modified model by introducing a new variable $θ$ that quantifies the sentiment of the investors. $θ=+1,~0,~-1$ for positive, neutral and negative sentiment, respectively.…
Large and stable indices of the world wide stock markets such as NYSE and SP 500 together with NASDAQ -- the index representing markets of new trends, and WIG -- the index of the local stock market of Eastern Europe, are considered. Due to the relation between artificial insymmetrised patterns (AIP) and time series, stationary and temporary properties of stock market indices are identified. By filtering extreme events it is found that fluctuations are self-similar. Snap-shots in time lead to estimates for a temporary state of a market with respect to its history. It appears that close to a cra…
The primary objective of this paper was to investigate whether the growth in the major US asset indices could be a function of the US broad money supply and/or US GDP, over the time period 2001 to 2019, using an information entropy methodology. The four US asset indices investigated were: (1) US National Property index; (2) Russell 2000 index; (3) S&P 500 index; and (4) NASDAQ index. Notwithstanding the financial crisis of 2007-2008, US real GDP increased exponentially over the period 2001 to 2019, with an average annual growth rate of approximately 2%. However, over this time period, the aver…
Following our previous investigation of the USA Standard and Poor index anti-bubble that started in August 2000, we analyze thirty eight world stock market indices and identify 21 anti-bubble. An ``anti-bubble'' is defined as a self-fulfilling decreasing price created by positive price-to-price feedbacks feeding overall pessimism and negative market sentiment further strengthened by inter-personal interactions. We mathematically characterize anti-bubbles by a power law decrease of the price (or of the logarithm of the price) as a function of time and by decelerating/expanding log-periodic osci…
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Levy-stable distribution L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot be expressed in a closed form, one can identify its parameters by testing the dependence of the central peak height on tau as well as the power-law decay of the tails. In an earlier study [Mantegna and Stanley, N…
Market prediction plays a major role in supporting financial decisions. An emerging approach in this domain is to use graphical modeling and analysis to for prediction of next market index fluctuations. One important question in this domain is how to construct an appropriate graphical model of the data that can be effectively used by a semi-supervised GNN to predict index fluctuations. In this paper, we introduce a framework called NETpred that generates a novel heterogeneous graph representing multiple related indices and their stocks by using several stock-stock and stock-index relation meas…
We study the cascading dynamics immediately before and immediately after 219 market shocks. We define the time of a market shock T_{c} to be the time for which the market volatility V(T_{c}) has a peak that exceeds a predetermined threshold. The cascade of high volatility "aftershocks" triggered by the "main shock" is quantitatively similar to earthquakes and solar flares, which have been described by three empirical laws --- the Omori law, the productivity law, and the Bath law. We analyze the most traded 531 stocks in U.S. markets during the two-year period 2001-2002 at the 1-minute time res…
Self-organized criticality has been claimed to play an important role in many natural and social systems. In the present work we empirically investigate the relevance of this theory to stock-market dynamics. Avalanches in stock-market indices are identified using a multi-scale wavelet-filtering analysis designed to remove Gaussian noise from the index. Here new methods are developed to identify the optimal filtering parameters which maximize the noise removal. The filtered time series is reconstructed and compared with the original time series. A statistical analysis of both high-frequency Nas…
This work addressed the use of the geometric Brownian motion to simulate the prices of shares listed in the Small Caps index of the Brazilian stock exchange B3 (Brazil, Bolsa, Balcão). The data used refer to the price history from January 2016 to December 2018. The price history of 2019 was used to be compared with the simulated prices. The data was imported from the Yahoo Finance database using the Python programming language, and the simulations were performed for each stock individually, and for portfolios formed based on expected returns, risk and the Sharpe Index. The results were better …
We present some indications of inefficiency of the Brazilian stock market based on the existence of strong long-time cross-correlations with foreign markets and indices. Our results show a strong dependence on foreign markets indices as the S\&P 500 and CAC 40, but not to the Shanghai SSE 180, indicating an intricate interdependence. We also show that the distribution of log-returns of the Brazilian BOVESPA index has a discrete fat tail in the time scale of a day, which is also a deviation of what is expected of an efficient equilibrated market. As a final argument of the inefficiency of the B…
Using data from 92 indices of stock exchanges worldwide, I analize the cluster formation and evolution from 2007 to 2010, which includes the Subprime Mortgage Crisis of 2008, using asset graphs based on distance thresholds. I also study the survivability of connections and of clusters through time and the influence of noise in centrality measures applied to the networks of financial indices.
In the age of globalization, it is natural that the stock market of each country is not independent form the other markets. In this case, collective behavior could be emerged form their dependency together. This article studies the collective behavior of a set of forty influential markets in the world economy with the aim of exploring a global financial structure that could be called world-stock-market network. Towards this end, we analyze the cross-correlation matrix of the indices of these forty markets using Random Matrix Theory (RMT). We find the degree of collective behavior among the mar…
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TA…
Summarized by the efficient market hypothesis, the idea that stock prices fully reflect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efficiency of stock markets, most studies assume this efficiency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we define the time-varying efficiency of stock markets by calculating the permutation entropy within sliding time-windows of log-returns of stock market indices. We show that major world stock …
Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We establish that this so-called gain/loss asymmetry is present also for individual stocks and show that the phenomenon is closely linked to the well-known leverage effect -- in the EGARCH model and a modified retarded volatility model, the same parameter that governs the magnitude of the leverage effect also governs the gain/loss asymmetry.
We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index alpha > 3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on high-frequency recordings of the S&P500, DAX and WIG20 indices over the interval May 2004 - May 2006. Our findings suggest that dynamics of the contemporary market may differ from the one observed in the past. This effect indicates a constantly increasing efficiency of world markets.
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR approach in order to get more robust results. We examine trends in CPR for an approximately 19-month window moved along the time series and compare them to ρ. Binning CPR into three levels of connectedness: strong, moderate and weak, we extract…
We investigate statistical properties of daily international market indices of seven countries, and high-frequency $S&P500$ and KOSDAQ data, by using the detrended fluctuation method and the surrogate test. We have found that the returns of international stock market indices of seven countries follow a universal power-law distribution with an exponent of $ζ\approx 3$, while the Korean stock market follows an exponential distribution with an exponent of $β\approx 0.7$. The Hurst exponent analysis of the original return, and its magnitude and sign series, reveal that the long-term-memory propert…
Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for different thresholds and diverse periods of time, so that it is then possible to analyze how clusters are formed according to correlations among indices and how they evolve in time, particularly during times of financial crises. Further analysis is made on the eigenvectors corresponding to the second highest eigenvalues of the correlation matrices, revealing a structure peculiar to markets that operate in different time zones.
In financial time series there are periods in which the value increases or decreases monotonically. We call those periods elemental trends and study the probability distribution of their duration for the indices DJIA, NASDAQ and IPC. It is found that the trend duration distribution often differs from the one expected under no memory. The expected and observed distributions are compared by means of the Anderson-Darling test.
We investigated the topological properties of stock networks through a comparison of the original stock network with the estimated stock network from the correlation matrix created by the random matrix theory (RMT). We used individual stocks traded on the market indices of Korea, Japan, Canada, the USA, Italy, and the UK. The results are as follows. As the correlation matrix reflects the more eigenvalue property, the estimated stock network from the correlation matrix gradually increases the degree of consistency with the original stock network. Each stock with a different number of links to o…
Modeling stock returns is not a new task for mathematicians, investors, and portfolio managers, but it remains a difficult objective due to the ebb and flow of stock markets. One common solution is to approximate the distribution of stock returns with a normal distribution. However, normal distributions place infinitesimal probabilities on extreme outliers, but these outliers are of particular importance in the practice of investing. In this paper, we investigate the normality of the distribution of daily returns of major stock market indices. We find that the normal distribution is not a good…
Herd behavior is an important economic phenomenon, especially in the context of the recent financial crises. In this paper, herd behavior in global stock markets is investigated with a focus on intercontinental comparison. Since most existing herd behavior indices do not provide a comparative method, we propose a new herd behavior index and demonstrate its desirable properties through simple theoretical models. As for empirical analysis, we use global stock market data from Morgan Stanley Capital International to study herd behavior especially during periods of financial crises in detail.
Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna's seminal paper, the linear Pearson's correlation coefficient between pairs of stocks has been the usual way to determine network edges. Recently, possible effects of nonlinearity on the graph-theoretical properties of such networks have been demonstrated when using nonlinear measures such as mutual information instead of linear correlation. In this paper, we quantitatively characterize the nonlinearity in stock time series and …
We perform non-linear analysis on stock market indices using time-dependent extended Tsallis statistics. Specifically, we evaluate the q-triplet for particular time periods with the purpose of demonstrating the temporal dependence of the extended characteristics of the underlying market dynamics. We apply the analysis on daily close price timeseries of four major global markets (S&P 500, Tokyo-NIKKEI, Frankfurt-DAX, London-LSE). For comparison, we also compute time-dependent Generalized Hurst Exponents (GHE) Hq using the GHE method, thus estimating the temporal evolution of the multiscaling ch…
COVID-19 has impacted the economy of almost every country in the world. Of particular interest are the responses of the economic indicators of developing nations (such as BRICS) to the COVID-19 shock. As an extension to our earlier work on the dynamic associations of pandemic growth, exchange rate, and stock market indices in the context of India, we look at the same question with respect to the BRICS nations. We use structural variable autoregression (SVAR) to identify the dynamic underlying associations across the normalized growth measurements of the COVID-19 cumulative case, recovery, and …
This study examines the monthly returns in Turkish and American stock market indices to investigate whether these markets experience abnormal returns during some months of the calendar year. The data used in this research includes 212 observations between January 1996 and August 2014. I apply statistical summary analysis, decomposition technique, dummy variable estimation, and binary logistic regression to check for the monthly market anomalies. The multidimensional methods used in this article suggest weak evidence against the efficient market hypothesis on monthly returns. While some months …
This paper concentrates on the time series momentum or contrarian effects in the Chinese stock market. We evaluate the performance of the time series momentum strategy applied to major stock indices in mainland China and explore the relation between the performance of time series momentum strategies and some firm-specific characteristics. Our findings indicate that there is a time series momentum effect in the short run and a contrarian effect in the long run in the Chinese stock market. The performances of the time series momentum and contrarian strategies are highly dependent on the look-bac…
The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend. These empirical asymmetries predict that stock index drops are more common on a relatively short time scale than the corresponding raises. We present several empirical examples of such asymmetries. Furthermore, a simple model featuring occasional short periods of synchronized dropping prices for all stocks constituting the index is introduced with the aim o…
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 compa…
