We apply RMT, Network and MF-DFA methods to investigate correlation, network and multifractal properties of 20 global financial indices. We compare results before and during the financial crisis of 2008 respectively. We find that the network method gives more useful information about the formation of clusters as compared to results obtained from eigenvectors corresponding to second largest eigenvalue and these sectors are formed on the basis of geographical location of indices. At threshold 0.6, indices corresponding to Americas, Europe and Asia/Pacific disconnect and form different clusters before the crisis but during the crisis, indices corresponding to Americas and Europe are combined together to form a cluster while the Asia/Pacific indices forms another cluster. By further increasing the value of threshold to 0.9, European countries France, Germany and UK constitute the most tightly linked markets. We study multifractal properties of global financial indices and find that financial indices corresponding to Americas and Europe almost lie in the same range of degree of multifractality as compared to other indices. India, South Korea, Hong Kong are found to be near the degree of multifractality of indices corresponding to Americas and Europe. A large variation in the degree of multifractality in Egypt, Indonesia, Malaysia, Taiwan and Singapore may be a reason that when we increase the threshold in financial network these countries first start getting disconnected at low threshold from the correlation network of financial indices. We fit Binomial Multifractal Model (BMFM) to these financial markets.
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable t…
Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both theoretical and practical point of view. Particularly, we discuss the methods based on estimation of Rényi entropy, which provide a powerful tool especially in presence of heavy-tailed data. To put some flesh on bare bones, all methods are compared on various real financial datasets, including daily and high-frequency data.
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves to evaluation of whether or not a time series is multifractal and width of the resulting singularity spectrum is considered a measure of the degree of complexity involved. However, the character of the complexity of time series generated by the natural processes usually appears much more intricate than such a bare statement can reflect. As an example, based…
Statistical and multiscaling characteristics of WTI Crude Oil prices expressed in US dollar in relation to the most traded currencies as well as to gold futures and to the E-mini S$\&$P500 futures prices on 5 min intra-day recordings in the period January 2012 - December 2017 are studied. It is shown that in most of the cases the tails of return distributions of the considered financial instruments follow the inverse cubic power law. The only exception is the Russian ruble for which the distribution tail is heavier and scales with the exponent close to 2. From the perspective of multiscaling t…
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…
Over the last two decades, financial systems have been studied and analysed from the perspective of complex networks, where the nodes and edges in the network represent the various financial components and the strengths of correlations between them. Here, we adopt a similar network-based approach to analyse the daily closing prices of 69 global financial market indices across 65 countries over a period of 2000-2014. We study the correlations among the indices by constructing threshold networks superimposed over minimum spanning trees at different time frames. We investigate the effect of criti…
Asymmetric relationship between price and volatility is a prominent feature of the financial market time series. This paper explores the price-volatility nexus in cryptocurrency markets and investigates the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes. The conventional GARCH-class models have shown that in cryptocurrency markets, asymmetric reactions of volatility to returns differ from those of other traditional financial assets. We address this issue from a viewpoint of fractal analysis, which can cover the nonlinear interactions and the self-s…
Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experi…
We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of Dow Jones Industrial Average and Financial Times Stock Exchange 100 in the period 1984-2013. Based on empirical results, we propose a bivariate version of the model, for which we find an explicit expression for the decay over time of cross-asset correlations between absolute returns. We compare our theoretical predictions with empirical estimates on the same…
We present a symmetry analysis of the distribution of variations of different financial indices, by means of a statistical procedure developed by the authors based on a symmetry statistic by Einmahl and Mckeague. We applied this statistical methodology to financial uninterrupted daily trends returns and to other derived observable. In our opinion, to study distributional symmetry, trends returns offer more advantages than the commonly used daily financial returns; the two most important being: 1) Trends returns involve sampling over different time scales and 2) By construction, this variable t…
This note examines financial distributions to competing teams at the end of the most famous multiple stage professional (male) bicyclist race, TOUR DE FRANCE. A rank-size law (RSL) is calculated for the team financial gains. The RSL is found to be hyperbolic with a surprisingly simple decay exponent (about equal to -1). Yet, the financial gain distributions unexpectedly do not obey Pareto principle of factor sparsity. Next, several (8) inequality indices are considered : the Entropy, the Hirschman-Herfindahl, Theil, Pietra-Hoover, Gini, Rosenbluth indices, the Coefficient of Variation and the …
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…
A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed method represents the indices as nodes in a directed graph, where the edges' weights are estimates of the pair-wise causal influences, quantified using the directed information functional. This method facilitates using a relatively small number of samples from each index. The ind…
This paper investigates the impact of COVID-19 on financial markets. It focuses on the evolution of the market efficiency, using two efficiency indicators: the Hurst exponent and the memory parameter of a fractional Lévy-stable motion. The second approach combines, in the same model of dynamic, an alpha-stable distribution and a dependence structure between price returns. We provide a dynamic estimation method for the two efficiency indicators. This method introduces a free parameter, the discount factor, which we select so as to get the best alpha-stable density forecasts for observed price r…
This paper uses new and recently introduced mathematical techniques to undertake a data-driven study on the systemic nature of global inflation. We start by investigating country CPI inflation over the past 70 years. There, we highlight the systemic nature of global inflation with a judicious application of eigenvalue analysis and determine which countries exhibit most "centrality" with an inner-product based optimization method. We then turn to inflationary impacts on financial market securities, where we explore country equity indices' equity robustness and the varied performance of equity s…
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…
