Detrending Moving-average Cross-correlation Research Articles

Effect of Futures Trading Restrictions on Market Efficiency: A Multifractal Analysis

Based on the China Securities Index 300 (CSI 300 index) futures trading restrictions in 2015, this paper uses the multifractal detrending moving-average cross-correlation analysis method (MF-X-DMA) to investigate the effect of introducing futures trading restrictions on the market efficiency of CSI 300 index spot and futures markets. We begin by using multifractal detrending moving-average analysis (MF-DMA) and find that the futures trading restrictions improve spot market efficiency but decrease futures market efficiency. Moreover, we examine the cross-correlation between spot and futures markets and the information transmission process. MF-X-DMA analysis shows an increase in the level of persistent cross-correlation between spot and futures markets, and a decrease in the multifractality degree of cross-correlation, suggesting that the relationship between spot and futures markets becomes stronger and less complicated after the futures trading restrictions. Moreover, the nonlinear Granger causality test shows that futures returns do not Granger cause spot returns after the restrictions. Therefore, the futures trading restrictions may mitigate the harmful effect of speculative trading in the futures market and thus improve spot market efficiency.

Analyzing interconnection among selected commodities in the 2008 global financial crisis and the COVID-19 pandemic

This study investigates the interconnection among several commodities in the advent of two well-known phenomena: the 2008 global financial crisis (GFC) and the COVID-19 pandemic. We use a daily return series for selected commodities: three base metals (copper, zinc, and lead), two benchmark crude oils (WTI and Brent), and gold. Three different methods have been considered to study interconnection: Multifractality, Network theory, and Wavelet coherences. By applying Detrending Moving-average Cross-correlation Analysis (DMCA) method, we witnessed an increase in cross-correlation in the higher time windows in most time series. Generally, we observe that the benchmark crude oils have the highest relationships, and then, in the following positions, we have the dependency among base metals (copper, lead, and zinc) and between the base metals and the crude oils. In the context of the Wavelet analysis, we notice that the significant fluctuations and changes in the extent of interconnections among data could be traced when the two crises occurred, particularly between October 2018 and April 2021, and in the frequency range of 4–128 days. This phenomenon indicates the role of the COVID-19 pandemic in creating a volatile situation in the commodity markets. The findings of this study have significant implications for investors, academic researchers, and policymakers.

How Statistically Significant is the DMCA Coefficient?

In this paper, we proposed a statistical test for the Detrending Moving-Average Cross-Correlation Coefficient ([Formula: see text]). With this methodology, it is possible to evaluate the statistical significance of [Formula: see text] for different confidence levels. The test was applied to financial market and climatological data. Findings on this research show that rejection or non-rejection of the null hypothesis of [Formula: see text] depends on the size [Formula: see text] of the series and the moving average window length [Formula: see text] evaluated. Our findings also show a behavioral pattern in the critical values of [Formula: see text]. Fixing the size of the series [Formula: see text], as the size of the moving average window length [Formula: see text] increases, the critical values tend to increase.

A portfolio strategy of stock market based on mean-MF-X-DMA model

In this study, the multifractal detrended moving-average cross-correlation analysis (MF-X-DMA) is combined with the Mean-Semi-Variance model to establish a Mean-MF-X-DMA model. This model is used to construct portfolio strategies by the stocks with the larger market value in each sector of the Standard and Poor's 500 Index (S&P 500). The empirical test shows that: firstly, there are long memory and obvious multifractal characteristics in each stock returns; secondly, the portfolio strategy based on Mean-MF-X-DMA model performs better than the traditional portfolio model, such as returns, Sharpe ratio, βcoefficient and utility for different risk preference investors; finally, the risk will be lower when the time scale is smaller under the same expected returns.

Uncovered interest rate parity through the lens of fractal methods: Evidence from the European Union

We study the uncovered interest rate parity in the European Union utilising the newly proposed regression frameworks based on the detrended cross-correlation analysis and the detrending moving-average cross-correlation analysis. The parity is analysed for three groups — the early Euro adopters, the later adopters, and the EU countries that are outside of the Eurozone. The main contributions of our study are twofold. First, we have analysed a large dataset that is not standard in the topical applied papers. And second, the utilised methods have allowed us to focus on possible differences between the short-term and long-term relationships between the interest rate differentials and foreign exchange rates that form the parity. Overall, the evidence for the parity is scarce, which is in hand with most of the previous studies. However, we have also uncovered some interesting patterns in the results and we provide an additional discussion of possible causes and directions for future research.

DCCA and DMCA correlations of cryptocurrency markets

We examine the serial correlation structure of six liquid cryptocurrencies with a long data record – Bitcoin, DASH, Stellar, Litecoin, Monero, and Ripple – with a use of the detrended cross-correlation (DCCA) and detrending moving-average cross-correlation (DMCA) correlation coefficients. We find that these cryptocurrencies behave differently from the stock markets which are much closer to the random walk (efficient) dynamics. We further discuss issues connected to strong statements about cryptocurrency markets practical inefficiency.

IDHS-DMCAC: identifying DNase I hypersensitive sites with balanced dinucleotide-based detrending moving-average cross-correlation coefficient

ABSTRACTDNase I hypersensitive sites (DHSs) are associated with regulatory DNA elements, so their good understanding is significant for both the biomedical research and the discovery of new drugs. Traditional experimental methods are laborious, time consuming and an inaccurately task to detect DHSs. More importantly, with the avalanche of genome sequences in the postgenomic age, it is highly essential to develop cost-effective computational approaches to identify DHSs. In this paper, we develop a statistical feature extraction model using the detrended moving-average cross-correlation (DMCA) coefficient descriptor based on dinucleotide property matrix generated by the 15 DNA dinucleotide properties, and this model is named iDHS-DMCAC. A 105-dimensional feature vector is constructed for a certain window on the two class imbalanced benchmark datasets, with over-sampling and support vector machine algorithms. Rigorous cross-validations indicate that our predictor remarkably outperforms the existing models in both accuracy and stability. We anticipate that iDHS-DMCAC will become a very useful high throughput tool, or at the very least, a complementary tool to the existing methods of identifying DNase I hypersensitive sites. The datasets and source codes of the proposed model are freely available at https://github.com/shengli0201/Datasets.

Relationship between onshore and offshore renminbi exchange markets: Evidence from multiscale cross-correlation and nonlinear causal effect analyses

Through multifractal detrended moving-average cross-correlation analysis (MF-X-DMA) and partial moving-average cross-correlation coefficient analysis (PDMCA), this paper studies power-law cross-correlations between renminbi (RMB) onshore and offshore markets (2013–2018). The interaction between CNY and CNH market pairs was examined with attention to how the floating exchange rate regime reform of August 11, 2015 affects their interactions. The obtained results suggest that net power-law cross-correlations exist between the CNY and CNH exchange markets (with influences of autocorrelation, interest rate difference, US Dollar, and Oil signals removed) and that the August 11, 2015 (referred to as “811”) exchange reform significantly affects the trend of multiscale cross-correlation coefficient curves. This study also verifies that the risk of offshore RMB markets in Europe and the UK is larger than in Hong Kong and the US when facing a large shock. The nonlinear causal effect analysis reveals that asymmetric bidirectional nonlinear causality exists between any market pair, and the degree of asymmetry appears to have declined after the 811 exchange rate regime reform. For the offshore RMB markets in the US, Europe, and UK, there is evidence of stronger causality running from the CNH to CNY than vice versa, which implies that the foreign impulses have had an influence on the domestic market, and the floating exchange rate reform effectively improves the RMB exchange rate formation mechanism.

Are cross-correlations between Turkish Stock Exchange and three major country indices multifractal or monofractal?

The analysis of linkages between financial markets has been a promising subject of study after globalization. Main consequence of these linkages is on transmission of the crisis from one country to another. Therefore, identifying and modeling of those linkages are important issues in the analysis of financial markets. According to studies the cross-correlations present nonlinear behavior and in general the well-known methods fail to predict such correlations. In this paper, we aim to show the existence of nonlinear cross-correlations between Turkish Stock Exchange and major developed country indices. For this purpose, we use the Multifractal Detrending Moving-Average Cross-correlation Analysis (MF-X-DMA) which is designed for detecting long-range power-law correlations. In the analysis we use the daily financial return and volatility series of Turkish stock market index BIST100 and developed market indexes which are S&P500, DAX30, FTSE100 for a period of 11 years between 01/01/2007-01/01/2018. The results show the existence of multifractality and long-range power-law cross-correlations.

Fractality in market risk structure: Dow Jones Industrial components case

We examine the Dow Jones Industrial Average index components with respect to the capital asset pricing model (CAPM), specifically its scaling properties in the sense of different investment horizons. To do so, we use the novel methods of fractal regressions based on the detrended cross-correlation analysis and the detrending moving-average cross-correlation analysis. We report three standard groups of stocks – aggressive, defensive and market-following – which are rather uniformly represented. For most of the stocks, the β parameter of the CAPM does not vary significantly across scales. There are two groups of exceptions. One of aggressive stocks which are even more aggressive for short investment horizons. These do not provide portfolio diversification benefits but allow for high profits above the market returns and even more so for the short investment horizons. And the other group of more defensive stocks which become very defensive in the long term. These stocks do not deliver short term profits but can serve as strong risk diversifiers. Apart from these direct results, our analysis opens several interesting questions and future research directions, both technical and experimental, which we discuss in more detail.

Power-law cross-correlations estimation under heavy tails

We examine the performance of six estimators of the power-law cross-correlations—the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator—under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the α-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.

Cross-correlations between volatility, volatility persistence and stock market integration: the case of emergent stock markets

In this paper, we investigate the dynamics of the two pairs of relationship, respectively volatility/market integration and volatility persistence/market integration, in the case of 20 emerging stock markets during the period 1999–2013. Employing the rolling windows approach we find that on most markets the persistent positive trend in volatility and volatility persistence is associated with the same trend in market integration. We use the detrending moving-average cross-correlation coefficients and we find positive cross-correlation that appears particularly in the long term and can only partly be attributed to the global financial crisis. The cross-section analysis shows that the markets which are more integrated display stronger volatility and volatility persistence, especially after 2005, when the level of market integration is higher. Our findings have several important implications for international portfolio management and security valuation.

Leverage effect in energy futures

We propose a comprehensive treatment of the leverage effect, i.e. the relationship between returns and volatility of a specific asset, focusing on energy commodities futures, namely Brent and WTI crude oils, natural gas and heating oil. After estimating the volatility process without assuming any specific form of its behavior, we find the volatility to be long-term dependent with the Hurst exponent on a verge of stationarity and non-stationarity. To overcome such complication, we utilize the detrended cross-correlation and the detrending moving-average cross-correlation coefficients and we find the standard leverage effect for both crude oils and heating oil. For natural gas, we find the inverse leverage effect. Additionally, we report that the strength of the leverage effects is scale-dependent. Finally, we also show that none of the effects between returns and volatility is detected as the long-term cross-correlated one. These findings can be further utilized to enhance forecasting models and mainly in the risk management and portfolio diversification.

Cross-correlations between the CSI 300 spot and futures markets

Financial markets are complex dynamical systems. One of the important features of market dynamics is the existence of cross-correlations between financial variables. Based on the high-frequency transaction prices (every 5 min) data, in this study, we investigate the cross-correlations between China Securities Index 300 (CSI 300) spot and futures markets. Qualitatively, employing a statistical test in analogy to the Ljung-Box test, we find that the cross-correlations are significant at the 1 % level. Quantitatively, using the multifractal detrending moving-average cross-correlation analysis (MF-XDMA) method, we find that the cross-correlations are strongly multifractal. An interesting finding is that the cross-correlation exponent is larger than the averaged generalized scaling exponent for different q, which is different from the general conclusion. Using the method of rolling windows, we find that the cross-correlations are positive over time, which suggests that China’s securities markets are not mature and efficient markets at present.

Multifractal detrending moving-average cross-correlation analysis

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents h(xy) extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q<0 and underperforms when q>0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of h(xy)(q) since its h(xy)(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.

A new approach to quantify power-law cross-correlation and its application to commodity markets

We proposed a new method: Detrended Moving-average Cross-correlation Analysis (DMCA) to detect the power-law cross-correlation between two correlated non-stationary time series by combining Detrended Cross-Correlation Analysis (DCCA) and Detrended Moving Average (DMA). In order to compare the performance of DMCA and DCCA in the detection of cross-correlation, and to estimate the influence of periodic trend, we generate two cross-correlated time series x(i) and y(i) by a periodic two-component fractionally autoregressive integrated moving average (ARFIMA) process. Then we apply both methods to quantify the cross-correlations of the generated series, whose theoretical values are already known to us. By comparing the results we obtained, we find that the performance of this new approach is comparable to DCCA with less calculating amounts; our method can also reduce the impact of trends; furthermore, DMCA (for background and forward moving average case) outperforms DCCA in more accurate estimation when the analyzed times series are short in length. To provide an example, we also apply this new method to the time series of the real-world data from Brent and WTI crude oil spot markets, to investigate the complex cross-market correlation between these commodity markets. In all, our method is another practical choice to detect the cross-correlation between two short period non-stationary time series, and has potential application to real world problems.