The Synchronization Effects of Stock Indices Dynamics in the Multifractal Analysis Using the Wavelet Technology (original) (raw)

Analysis of Stock Market Indices with Multidimensional Scaling and Wavelets

Stock market indices SMIs are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling MDS. Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

Wavelet Transform Modulus Maxima Approach for World Stock Index Multifractal Analysis

Information Technology and Management Science, 2012

This paper describes an approach that is able to fix difference in multifractal behaviour of various World Stock Indexes. The approach is beneficial for the forecasting and simulations of the most European and Asian stock indexes. Multifractal analysis is provided using the so-called Wavelet Transform Modulus Maxima approach, which involves two basic aspects:

Comovement of Selected International Stock Market Indices:A Continuous Wavelet Transformation and Cross Wavelet Transformation Analysis

2013

This study accounts for the time-varying pattern of price shock transmission, exploring stock market co-movements using continuous wavelet coherency methodology to find the correlation analysis between stock market indices of Malaysia, Thailand (Asian), Greece (Europe) and United States, in the time-frequency domain of time-series data. We employ the Wavelet Coherence method with the consideration of the financial crisis episodes of 1997 Asian Financial Crisis, 1998 Russian Sovereign Debt Default, 9/11 Attack on World Trade Centre US, 2008 US Sub-Prime Mortgage Crisis and the recent 2010-2011 Greece Debt Crisis. Results tend to indicate that the relations among indices are strong but not homogeneous across time scales, that local phenomena are more evident than others in these markets and that there seems to be no quick transmission through markets around the world, but a significant time delay. The relations among these indices have changed and evolved through time, mostly due to the financial crises that occurred at different time periods. Results also favour the view that regionally and economically closer markets exhibit higher correlation and more short run comovements among them. The high correlation between the two regional indices of Malaysia and Thailand, indicates that for the international investors, it is little gain to include both in their portfolio diversification. Strong co-movement is mostly confined to long-run fluctuations favouring contagion analysis. This indicates that shocks in the high frequency but low period are short term but shocks in the low frequency but high period are long term with the trend elements affecting the co-movements of the indices. The study of market correlations on the frequency-time scale domain using continuous wavelet coherency is appealing and can be an important tool in decision making for different types of investors.

Correlation, Network and Multifractal Analysis of Global Financial Indices

RePEc: Research Papers in Economics, 2012

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.

Multifractal analysis and instability index of prior-to-crash market situations

We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates. These spectra have properties that typify the prior-to-crash market situation. Any of these spectra entail elaborate processing of the raw signal data. With the unprocessed raw data we obtain an instability index, also with properties that typify the prior-to-crisis market situation. Both spectra and the instability index agree in characterizing such crashes, and in giving an early warning of them.

Role of multifractal sources in the analysis of stock market time series

Physica A: Statistical Mechanics and its Applications, 2005

It has been repeatedly reported that time series of returns in stock markets are of multifractal (multiscaling) character. Recently, a direct geometrical framework, much more revealing about the underlying dynamics than usual statistical approaches, has been introduced. In this paper we use this geometrical method to undercover several aspects that concern the dynamics of stock market time series. We introduce and discuss a new, powerful processing tool, namely the computation of sources. With the aid of the source field, we will separate the fast, chaotic dynamics defined by the multifractal structure from a new, so-far unknown slow dynamics which concerns long cycles in the series. We discuss the results on the perspective of detection of sharp dynamic changes and forecasting. r

Multifractal analysis of Asian markets during 2007–2008 financial crisis

Physica A: Statistical Mechanics and its Applications, 2015

h i g h l i g h t s • We study the US and Asian markets during 2007-2008 crisis triggered by the US subprime loans. • A study of markets during a crisis could reveal important information about their dynamics. • Markets of the US, Japan, Hong Kong, Korea and Indonesia show strong nonlinearities for positive q. • These nonlinearities are due to long range correlations of large fluctuations in returns. • The tail exponent of the cumulative log return distribution decreases during the crisis period. a b s t r a c t 2007-2008 US financial crisis adversely affected the stock markets all over the world.

Comovement of Central European stock markets using wavelet coherence: Evidence from high-frequency data

2011

In this paper, we contribute to the literature on international stock market comovement. The novelty of our approach lies in usage of wavelet tools to highfrequency financial market data, which allows us to understand the relationship between stock market returns in a different way. Major part of economic time series analysis is done in time or frequency domain separately. Wavelet analysis can combine these two fundamental approaches, so we can work in time-frequency domain. Using wavelet power spectra and wavelet coherence, we have uncovered interesting dynamics of cross-correlations between Central European and Western European stock markets using high-frequency data. Our findings provide possibility of a new approach to financial risk modeling.

Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

SSRN Electronic Journal, 2004

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities in the distribution of market returns over time and thereby of the kind of uncertainty or "randomness" in a particular market. Changes in this multifractal spectrum display distinctive patterns around substantial market crashes or "drawdowns." In other words, the kinds of singularities and the kinds of irregularity change in a distinct fashion in the periods immediately preceding and following major market drawdowns. This paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding different crashes at different times, we do find the same uniquely identifiable pattern in various stock markets experiencing the same crash at the same time. Moreover, our results suggest that all such crashes are preceded by a gradual increase in the weighted average of the values of the Lipschitz regularity exponents, under low dispersion of the multifractal spectrum. At a crash, this weighted average irregularity value drops to a much lower value, while the dispersion of the spectrum of Lipschitz exponents jumps up to a much higher level after the crash. Our most striking result, however, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5 < H < 0.7, these spectra tend to be skwed towards anti-persistence in the returns.

Wavelet Analysis of Central European Stock Market Behaviour During the Crisis

2009

In the paper we test for the different reactions of stock markets to the current financial crisis. We focus on Central European stock markets, namely the Czech, Polish and Hungarian ones, and compare them to the German and U.S. benchmark stock markets. Using wavelet analysis, we decompose a time series into frequency components called scales and measure their energy contribution. The energy of a scale is proportional to its wavelet variance. The decompositions of the tested stock markets show changes in the energies on the scales during the current financial crisis. The results indicate that each of the tested stock markets reacted differently to the current financial crisis. More important, Central European stock markets seem to have strongly different behaviour during the crisis.