Detrended Cross-correlation Analysis Research Articles

A Multifractal Cross-Correlation Analysis of Economic Policy Uncertainty: Evidence from China and US

In this study, we utilized the prevailing economic policy uncertainty index (EPU) as the proxy of state economic fluctuation and investigated Sino–US economic fluctuation long horizon cross-correlation with a multifractal detrended cross-correlation analysis (MF-DCCA). With the MF-DCCA approach, we found a reliable long-range cross-correlation between China and US EPU changes. In addition, we discovered that a power law cross-correlation existed for the variation of most scaling orders. However, no persistence of cross-correlations was detected within the Sino–US EPU change series. Additionally, we implemented Rényi exponent and spectrum singularity checks. Both the examination results proved series multifractality with the presented arch-shaped curves. We further calculated the Hölder exponent bounds within each series and found that the China EPU changes had maximal multifractality with the largest exponent difference.

Economic Policy Uncertainty and Stock Markets: A Multifractal Cross-Correlations Analysis

We utilize the multifractal detrended cross-correlation analysis (MF-DCCA) to investigate the cross-correlations between the US economic policy uncertainty (EPU) and US stock markets in the framework of Fractal Market Hypothesis (FMH). The data contain daily closing values of EPU, and the returns of Dow Jones Industrial Average Index (DJI), S&P 500 index (GSPC) and NASDAQ Composite Index (IXIC). Our empirical results show that changes in EPU and fluctuations in the US stock markets interact in a nonlinear way. Furthermore, there exists significant multifractality in the cross-correlations between EPU and stock markets. The cross-correlations exhibit dynamics and are affected by major international events. We capture the underlying mechanisms such as multifractality and nonlinear relation that dominate EPU-US stock markets nexus by means of FMH. The findings add a new dimension to the existing literature, and are important for market participants to adjust investment decisions.

Cross-correlations between price and volume in China's crude oil futures market: A study based on multifractal approaches

Abstract In this paper, we investigate the multifractal characteristics of the cross-correlations between price and volume in China's first crude oil futures market (INE), and compared the INE market with Brent and WTI market. Multifractal detrended cross-correlation analysis (MF-DCCA) was applied to comprehensively research the multifractal characteristics of the three different crude oil futures markets based on the data of the past five years. The results show that the cross-correlations between price change and volume change have significant multifractal characteristics in three markets, and the degree of multifractality is stronger in the WTI market for the full sample. Due to the INE market appeared late, the sample size of INE is not consistent with that of the other two markets. In order to solve this influence, we further compare the multifractal characteristics of the three crude oil futures markets in the same period (March 26, 2018 to November 20, 2020) and compares the results with those of the full sample period. The empirical results show that the degree of multifractality in both Brent and WTI markets is increased. To further verify whether this result is due to the emergence of the INE crude oil market, the entire sample of the Brent and WTI markets are divided into two periods according to the launch time of INE market. The result shows that the degree of multifractality and the risk of these two markets are all stronger in the last two years. Thus, there are reasons to believe that the emergence of INE market has a certain impact on the traditional Brent and WTI market, and a greater impact on Brent market. However, MFDCCA only consider the overall situation and cannot describe the multifractal cross-correlation between the upward and downward trends of the market. Thus, it probably won't accurately reflect the nonlinear cross-correlation. Furthermore, we study the characteristics of the asymmetric multifractal cross-correlations in different trends (upwards or downwards) by using the multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) method. Empirical results indicate that the cross-correlation between price and volume in three markets shows obvious asymmetry. Specifically, when the price changes series is on an upward trend, or when the volume changes series is on a downward trend, the degree of asymmetry in three markets is stronger, and the risk situation of the market is more complex. Therefore, for a portfolio of assets with different markets, investors should fully observe and understand different market trends and make reasonable investment based on their own risk preference.

COVID-19 pandemic and global financial market interlinkages: a dynamic temporal network analysis

ABSTRACT The present study investigates the changes in G20 stock market dynamics and their interlinkages in the aftermath of COVID-19. It utilizes the Detrended Cross-Correlation Analysis (DCCA) along with the network and complexity theories for detecting the contagion effect of the pandemic on the stock markets. We find that both advanced and emerging stock markets, departing from their pre-crisis structures, form a tightly coupled close community after the disease outbreak – except for China that distanced itself from the rest of the cohort. This indicates that COVID-19 has caused contagion in the global equity market, which has increased the risk to international portfolio diversification benefits. The adoption of the Network theory for contagion detection technique augments the detailed understanding of the structural changes and their interlinkages among the stock markets in a more comprehensive way.

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.

Extended Methodology for DFA and DCCA: Application of Automatic Search Procedure and Correlation Map to the Weierstrass-Mandelbrot Functions.

Detrended fluctuation analysis and detrended cross-correlation analysis are used in this study to identify and characterize correlated data. The objective of these two techniques is to separate different fluctuations from the contributions due to external trends by evaluating the autocorrelation and cross-correlation exponents, in order to determine if scale properties persist with the size of the series. Two new methodologies were extended from cross-correlation coefficients for local analysis, which we call the \textit{automatic search procedure.

Analysis of Collective Response Reveals that COVID-19-Related Activities Start from the End of 2019 in Mainland China

While the COVID-19 outbreak is making an impact at a global scale, the collective response to the pandemic becomes the key to analyzing past situations, evaluating current measures, and formulating future predictions. In this paper, we analyze the public reactions to the pandemic using search engine data and mobility data from Baidu Search and Baidu Maps respectively, where we particularly pay attention to the early stage of pandemics and find early signals from the collective response to COVID-19. First, we correlate the number of confirmed cases per day to daily search queries of a large number of keywords through Dynamic Time Warping (DTW) and Detrended Cross-Correlation Analysis (DCCA), where the keywords top in the most critical days are believed the most relevant to the pandemic. We then categorize the ranking lists of keywords according to the specific regions of the search, such as Wuhan, Mainland China, the USA, and the whole world. Through the analysis on search, we succeed in identifying COVID-19 related collective response would not be earlier than the end of 2019 in Mainland China. Finally, we confirm this observation again using human mobility data, where we specifically compare the massive mobility traces, including the real-time population densities inside key hospitals and inter-city travels departing from/arriving in Wuhan, from 2018 to 2020. No significant changes have been witnessed before December, 2019.

Study on the cross-correlation between two country for soybean futures price and exchange rate

The paper investigates the connection between two countries’ foreign exchange and futures market for soybean, DCE NO.1 soybean and CBOT soybean as the research object by using multifractal detrended cross-correlation analysis (MF-DCCA). Results indicate a significant multifractal cross-correlation among USDCNY and two country’s soybean futures. By contrasting the multifractality of the original series to processed series, we discover that the fat-tailed distribution serves as the primary cause for USDCNY-DCE sets while the long-range correlation explains the other. Our result shows that the soybean futures in China has a higher multifractality degree, but the fluctuation of exchange rate has a better pass-through effect on the price of US soybean futures’ market.

Analyzing the Impact of COVID-19 on the Cross-Correlations between Financial Search Engine Data and Movie Box Office

This paper explores the COVID-19 influences on the cross-correlation between the movie market and the financial market. The nonlinear cross-correlations between movie box office data and Google search volumes of financial terms such as Dow Jones Industrial Average (DJIA), NASDAQ and PMI are investigated based on multifractal detrended cross-correlation analysis (MF-DCCA). The empirical results show there are nonlinear cross-correlations between movie market and financial market. Metrics such as Hurst exponents, singular exponents and multifractal spectrum demonstrate that the cross-correlation between movie market and financial market is persistent, and the cross-correlation in long term is more stable than that in short term. In the COVID-19 period, the multifractal features of cross-correlation become stronger implying that COVID-19 enhanced the complexity between the movie industry and the financial market. Furthermore, through the rolling window analysis, the Hurst exponent dynamic trends indicate that COVID-19 has a clear influence on the cross-correlation between movie market and financial market.

Multifractal Fluctuation Analysis of Correlations Between the Sector Stock Markets in China and the US

With the rapid development of economic globalization, the stock markets in China and the US are increasingly linked. The fluctuation features and cross-correlations of the two countries’ markets have attracted extensive attention from market investors and researchers. In this paper, the fractal analysis methods including multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) and coupled detrended cross-correlation analysis (CDCCA) are applied to explore the volatilities of CSI300 and SP500 sector stock indexes as well as the cross-correlations and coupling cross-correlations between the two corresponding sector stock indexes. The results show that the auto-correlations, cross-correlations and coupling cross-correlations have multifractal fluctuation characteristics, and that the cross-correlations are asymmetric. Additionally, the coupling cross-correlation strengths are distinct due to the different influence of long-range correlations and fat-tailed distribution. Further, the co-movement between China and the US sector stock markets is susceptible to external market factors such as major economic events and national policies.

Joint Multifractal Analysis and Source Testing of River Level Records Based on Multifractal Detrended Cross-Correlation Analysis

The joint multifractal analysis is usually conducted in two different variables for their cross-correlations but rarely used for two records of one variable collected at two different places. It is important for the detection of change in multifractality in space. Besides, the cross-correlations in two analyzed series make the analysis of sources of joint multifractality difficult. There are few studies on the source of joint multifractality. We focus on the two issues for two level records at pairs of adjacent sites along one river and carry out an extension of our previous work which is about the single multifractality of one record with the same data set. The data set is collected from 10 observation stations of a northern China river and contains about two million high-frequency river level records. Results of joint multifractal analysis via multifractal detrended cross-correlation analysis show that the change in joint multifractality at pairs of adjacent sites caused by weak cross-correlations can be detected by comparing the single generalized Hurst exponent with the joint scaling exponent function and reveal the effects of human activities on joint multifractality. This analysis provides an approach for detecting the change in multifractality. Following the idea of our previous work, two robust hypothesis tests via a set of pairs of surrogate series are proposed for the source testing of joint multifractality. The analysis of the effects of cross-correlations is carried out via a proposed simultaneously half-shifting technique which can both minimize the cross-correlations between original series and make full use of records. Results of source analysis show not only the effects of autocorrelations in series and probability distribution of river levels but also the effects of cross-correlations between series.

Hedging effectiveness of Chinese Treasury bond futures: New evidence based on nonlinear analysis

Using multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DCCA) methods, this paper investigates the hedging effectiveness of Chinese Treasury bond futures. We utilize MF-DFA approach and show that Treasury bond spot and futures markets are multifractal. Moreover, results based on MF-DCCA suggest persistent cross-correlation between 10-year Treasury bond spot and futures, but no significant cross-correlation between 5-year Treasury bond spot and futures. Interestingly, there also exists persistent cross-correlation between 10-year Treasury bond futures and other Treasury bonds (5-year and long-term). Results based on MF-CCA verify the persistent cross-correlations above. Our findings imply that 10-year Treasury bond futures contracts can serve as better tools to hedge interest rate risk.

On the behavior of the DFA and DCCA in trend-stationary processes

In this work, we develop the asymptotic theory of the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) for trend-stationary stochastic processes without any assumption on the specific form of the underlying distribution. All results are presented and derived under the general framework of potentially overlapping boxes for the polynomial fit. We prove the stationarity of the DFA and DCCA, viewed as stochastic processes, obtain closed forms for moments up to second order, including the covariance structure for DFA and DCCA and a miscellany of law of large number related results. Our results generalize and improve several results presented in the literature. To verify the behavior of our theoretical results in small samples, we present a Monte Carlo simulation study and an empirical application to econometric time series.

Age-related alterations on the capacities to navigate on a bike: use of a simulator and entropy measures.

Studying the impact of age is important to understand the phenomenon of aging and the disorders that are associated with it. In this work, we analyze age-related alterations on the capacities to navigate on a bike. For this purpose, we use CycléoONE, a bike simulator, and entropy measures. We thus record navigation data (handlebar angle and speed) during the ride. They are processed with two cross-distribution entropy methods (time-shift multiscale cross-distribution entropy and multiscale cross-distribution entropy). We also analyze the time series with a detrended cross-correlation analysis to determine which method can best underline age-related alterations. Our results show that methods based on cross-distribution entropy may be efficient to stress the decrease in navigation capacities with age. The results are very encouraging for our future goal of adding medical benefits to a leisure equipment. They also show the value of using virtual reality to study the impact of age. Graphical Abstract This study deals with the use of the signal processing methods (multiscale cross-entropy and multiscale cross-correlation) applied on naviagtion data, acquired with a bike simulator, to study the impact of age on two populations (young healthy subjects and older adults with loss of autonomy).

Research on the portfolio model based on Mean-MF-DCCA under multifractal feature constraint

In order to incorporate the multifractal characteristics of the capital market into the research framework of portfolios and overcome the shortcomings of existing research results that had not considered the existence of multiple fractal fluctuation characteristics and multiple fractal correlation characteristics of asset prices, in this paper, multifractal detrended cross-correlation analysis (MF-DCCA) was embedded into the mean–variance criterion, the Mean-MF-DCCA portfolio model was constructed under the constraints of multiple fractal features, and the analytical solution of the model was given. On this basis, the effectiveness of Mean-MF-DCCA portfolio model was tested using empirical analysis. The results showed that the Mean-MF-DCCA portfolio model was effective, and compared with the mean–variance portfolio model, it is more conducive to investors to construct a sophisticated portfolio under the multiple fluctuation importance degree and multiple time scales, so as to improve their portfolio performance.

PORTFOLIO MODEL UNDER FRACTAL MARKET BASED ON MEAN-DCCA

Under the realistic background that the capital market nowadays is a fractal market, this paper embeds the detrended cross-correlation analysis (DCCA) into the return-risk criterion to construct a Mean-DCCA portfolio model, and gives an analytical solution. Based on this, the validity of Mean-DCCA portfolio model is verified by empirical analysis. Compared to the mean-variance portfolio model, the Mean-DCCA portfolio model is more conducive for investors to build a sophisticated investment portfolio under multi-time-scale, improve the performance of portfolios, and overcome the defect that the mean-variance portfolio model has not considered the existence of fractal correlation characteristics between assets.

Multifractal detrended cross-correlation analysis of wind speed and solar radiation.

In this work, the multifractal properties of wind speed and solar radiation are studied in a small region in which a wide variety of micro-climates are concentrated. To achieve this, two years of hourly data are analyzed in Guadeloupe archipelago. The four selected stations for wind speed were chosen according to trade winds direction, while solar radiation is recorded at a representative location at the center of the island. First, the results of the multifractal detrended fluctuation analysis (MF-DFA) showed the multifractal and persistent behaviors of wind speed at all locations. Due to the continental effect that increases along the transect, the Hurst exponent (H) values decrease from east to west. In addition, the MF-DFA clearly highlighted the presence of a nocturnal radiative layer that weakens wind speed in the surface layer. The multifractality degree [Δh(q)] values confirm the peculiarity of wind speed regimes at the center of the island. Thereafter, the MF-DFA results of solar radiation exhibited its multifractal and persistent behavior. Due to the solar radiation planetary scale, its Δh(q) is lower than those obtained for wind speed, which strongly depends on synoptic and local scales. The source of multifractality of wind speed and solar radiation is due to correlations of small and large fluctuations. Finally, the results of the multifractal detrended cross-correlation analysis between wind speed and solar radiation pointed out that the multifractal cross-correlation degree [Δhxy(q)] is identical for each site, which is not the case for Hurst exponent values.

Multifractal Analysis of Market Efficiency across Structural Breaks: Implications for the Adaptive Market Hypothesis

The primary objective of this paper is to assess the behavior of long memory in price, volume, and price-volume cross-correlation series across structural breaks. The secondary objective is to find the appropriate structural breaks in the price series. The structural breaks in the series are identified using the Bai and Perron procedure, and in each segment, Multifractal Detrended Fluctuation Analysis (MFDFA) and Multifractal Detrended Cross-Correlation Analysis (MFDCCA) are conducted to capture the long memory in each series. The price series is persistent in small fluctuations and anti-persistent in large fluctuations across all the structural segments. This confirms that long memory in the series is not affected by the structural breaks. Both volume and price-volume cross-correlation are anti-persistent in all the structural segments. In other words, volume acts as a carrier of the information only in the non-volatile (normal) market. The varying Hurst exponent across the structural segments indicates the varying levels of persistence and signifies the volatile market. The findings of the study are useful for understanding the practical implications of the Adaptive Market Hypothesis (AMH).

The instrument fault detection and identification based on kernel principal component analysis and coupling analysis in process industry

This paper investigates the fault detection problem of instruments in process industry. Considering the difficulty of fault identification and the problems of multivariable and large computation complexity based on traditional kernel principal component analysis (KPCA), this paper presents a new method for fault detection and identification, which combines the coupling analysis with kernel principal component for multivariable fault detection and employed the local outlier factor (LOF) for multivariable fault identification. The new method consists of three parts. Firstly, according to nonlinear correlation of multivariable, coupling analysis and module division of variables based on detrended cross-correlation analysis (DCCA) are considered to reduce false alarm rate (FAR) and missed detection rate (MDR) in fault detection and identification. Secondly, KPCA is employed to detect fault in each sub-module of variables. Finally, for the sub-module which has the fault detected in second step, the LOF is adopted to calculate abnormal contribution of each variable in sub-modules to realize fault identification. To prove that the new method has the better capability of processing multivariable fault detection and the more accuracy rate on fault detection and identification than the conventional methods of KPCA, a case study on Tennessee process is carried out at the end.

Segment Stock Market, Foreign Investors, and Cross-Correlation: Evidence from MF-DCCA and Spillover Index

Employing the tools of multifractal detrended cross-correlation analysis (MF-DCCA) and Diebold–Yilmaz spillover index (D.Y. spillover index), we examine the effect that the foreign investors have on the cross-correlations between the two-segment stock markets, that are the accessible and the inaccessible stock markets, and the other ten respective stock markets. The shares cross-listed by the same corporates on both the A-share and H-share stock markets of China serve as the best sample to compile the two stock indices, which stands for the inaccessible stock market (AHA) and the accessible stock market (AHH), respectively. Empirical results show that the cross-correlations between the two-segment stock markets and the other ten pairs are multifractal, the multifractal strength of cross-correlations is stronger in AHH than AHA, and the intensified growth of the multifractal cross-correlations in AHA can be seen as the increasing of the openness in the inaccessible market. The empirical result of D.Y. spillover index is consistent with the multifractal analysis above, and another interesting finding is that among the selected markets, the three markets with the strongest spillover effects with AHA and AHH are Taiwan, South Korea, and Singapore, respectively, and the weakest one is Australia during the sample scenarios.