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This paper sets out to solve a common and crucial fundamental theoretical problem of gray incidence cluster analysis: to [X]={X|ρ(X,Y)≥1−ε0} constitute an approximate classification, it must first be proven that [X]={X|ρ(X,Y)=1} constitutes a rigorous classification.

This paper does not study the concrete expressions of various incidence degrees but rather the perfect correlation essence of such incidence degrees, that is, sufficient and necessary conditions.

For any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree, it is proven that the perfect correlation relation is an equivalence relation. The set composed of all sequences Y that are equivalent to sequences X is studied, that is, the equivalence class of X. The structure and mutual relations of these equivalence classes are discussed, and the topological homeomorphism concept of incidence degree is introduced. The conclusion is obtained that the equivalence classes of the two incidence degrees must be the same when the topological homeomorphism is obtained.

In this paper, only the perfect correlation relation of any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree are studied as equivalent relations.

Not only are the research results of several incidence degrees involved in this paper original but also many other effective incidence degrees have not done this basic research, so this paper opens up a research direction with theoretical significance.

This study aims to modify the human factors analysis and classification system (HFACS) to make it suitable for collapse accident analysis in construction. Based upon the modified HFACS, distribution patterns of causal factors across multiple levels were discerned among causal factors of various stakeholders at construction sites. It explored the correlations between two causal factors from different levels and further determined causation paths from two perspectives of level and stakeholder.

The main research framework consisted of data collection, coding and analysis. Collapse accident reports were collected with adequate causation information. The modified HFACS was utilized for coding causal factors across all five levels in each case. A hybrid approach with two perspectives of level and stakeholder was proposed for frequency analysis, correlation analysis and path identification between causal factors.

Eight causal factors from external organizations at the fifth level were added to the original HFACS. Level-based correlation analyses and path identification provided safety managers with a holistic view of inter-connected causal factors across five levels. Stakeholder-based correlation analyses between causal factors from the fifth level and its non-adjacent levels were implemented based on client, government and third parties. These identified paths were useful for different stakeholders to develop specific safety plans for avoiding construction collapse accidents.

This paper fulfils an identified need to modify and utilize the HFACS model for correlation analysis and path identification of causal factors resulting in collapse accidents, which can provide opportunities for tailoring preventive and protective measures at construction sites.

This study proposes a novel method utilising a speech-word pair bipartite network to examine the correlation structure between members of parliament (MPs) in the context of the UK- China relationship.

We construct MP-word pair bipartite networks based on the co-occurrence relationship between MPs and words in their speech content. These networks are then mapped into monopartite MPs correlation networks. Additionally, the study calculates correlation network indicators and identifies MP communities and factions to determine the characteristics of MPs and their interrelation in the UK-China relationship. This includes insights into the distribution of key MPs, their correlation structure and the evolution and development trends of MP factions.

Analysis of the parliamentary speeches on China-related affairs in the British Parliament from 2011 to 2020 reveals that the distribution and interrelationship of MPs engaged in UK-China affairs are centralised and discrete, with a few core MPs playing an integral role in the UK-China relationship. Among them, MPs such as Lord Ahmad of Wimbledon, David Cameron, Lord Hunt of Chesterton and Lord Howell of Guildford formed factions with significant differences; however, the continuity of their evolution exhibits unstableness. The core MP factions, such as those led by Lord Ahmad of Wimbledon and David Cameron, have achieved a level of maturity and exert significant influence.

The research has several limitations that warrant acknowledgement. First, we mapped the MP-word pair bipartite network into the MP correlation network for analysis without directly analysing the structure of MPs based on the bipartite network. In future studies, we aim to explore various types of analysis based on the proposed bipartite networks to provide more comprehensive and accurate references for studying UK-China relations. In addition, we seek to incorporate semantic-level analyses, such as sentiment analysis of MPs, into the MP-word -pair bipartite networks for in-depth analysis. Second, the interpretations of MP structures in the UK-China relationship in this study are limited. Consequently, expertise in UK-China relations should be incorporated to enhance the study and provide more practical recommendations.

Firstly, the findings can contribute to an objective understanding of the characteristics and connotations of UK-China relations, thereby informing adjustments of focus accordingly. The identification of the main factions in the UK-China relationship emphasises the imperative for governments to pay greater attention to these MPs’ speeches and social relationships. Secondly, examining the evolution and development of MP factions aids in identifying a country’s diplomatic focus during different periods. This can assist governments in responding promptly to relevant issues and contribute to the formulation of effective foreign policies.

First, this study expands the research methodology of parliamentary debates analysis in previous studies. To the best of our knowledge, we are the first to study the UK-China relationship through the MP-word-pair bipartite network. This outcome inspires future researchers to apply various knowledge networks in the LIS field to elucidate deeper characteristics and connotations of UK-China relations. Second, this study provides a novel perspective for UK-China relationship analysis, which deepens the research object from keywords to MPs. This finding may offer important implications for researchers to further study the role of MPs in the UK-China relationship.

This study proposes a novel scheme for analysing the correlation structure between MPs based on bipartite networks. This approach offers insights into the development and evolving dynamics of MPs.

This paper aims to empirically investigate time–frequency linkages between Euramerican mature and Asian emerging crude oil futures markets in terms of correlation and risk spillovers.

With daily data, the authors first undertake the MODWT method to decompose yield series into four different timescales, and then use the R-Vine Copula-CoVaR to analyze correlation and risk spillovers between Euramerican mature and Asian emerging crude oil futures markets.

The empirical results are as follows: (a) short-term trading is the primary driver of price volatility in crude oil futures markets. (b) The crude oil futures markets exhibit certain regional aggregation characteristics, with the Indian crude oil futures market playing an important role in connecting Euramerican mature and Asian emerging crude oil futures markets. What’s more, Oman crude oil serves as a bridge to link Asian emerging crude oil futures markets. (c) There are significant tail correlations among different futures markets, making them susceptible to “same fall but different rise” scenarios. The volatility behavior of the Indian and Euramerican markets is highly correlated in extreme incidents. (d) Those markets exhibit asymmetric bidirectional risk spillovers. Specifically, the Euramerican mature crude oil futures markets demonstrate significant risk spillovers in the extreme short term, with a relatively larger spillover effect observed on the Indian crude oil futures market. Compared with India and Japan in Asian emerging crude oil futures markets, China's crude oil futures market places more emphasis on changes in market fundamentals and prefers to hold long-term positions rather than short-term technical factors.

The MODWT model is utilized to capture the multiscale coordinated motion characteristics of the data in the time–frequency perspective. What’s more, compared to traditional methods, the R-Vine Copula model exhibits greater flexibility and higher measurement accuracy, enabling it to more accurately capture correlation structures among multiple markets. The proposed methodology can provide evidence for whether crude oil futures markets exhibit integration characteristics and can deepen our understanding of connections among crude oil futures prices.

Understanding correlations between stock and direct real estate returns, which is the key factor that determines diversification benefits in a portfolio, helps formulate and implement better investors' asset allocation and risk management strategies. The past studies find that direct real estate returns have a low unconditionally (long‐run) correlation with the returns of equities. However, assuming that such correlation is constant throughout all periods is implausible. The purpose of this study is to test the time‐varying correlations of returns between general stocks and direct real estate.

This study uses the dynamic conditional correlation (DCC) model, which is a simplified version of the multivariate generalised autoregressive conditional heteroskedasticity (GARCH) model, proposed by Engle to test the time‐varying correlations between stock and direct real estate returns in six markets, which include the USA, the UK, Ireland, Australia, Hong Kong and Singapore.

The empirical results show significant time‐varying effects in the conditional covariance between stock returns and direct real estate returns. The results vary across different real estate sub‐sectors, and across different countries. It is observed that the conditional covariance increases in the boom markets, but becomes weaker in the post‐crisis periods. The authors observed significant jumps in the conditional covariance between the two asset markets in Singapore and Hong Kong in the post‐1977 Asian Financial crisis periods and in the post‐2007 US Sub‐prime crisis periods.

The past studies find that direct real estate returns have a low unconditionally (long‐run) correlation with the returns of equities. However, assuming that such correlation is constant throughout all periods is implausible. This study fills in the gap by using the dynamic conditional correlation models to allow for time‐varying effects in the correlations between stock and real estate returns.

The purpose of this paper is to reveal the multi‐scale relation between power law distribution and correlation of stock returns and to figure out the determinants underlying capital markets.

The multi‐scale relation between power law distribution and correlation is investigated by comparing the original series with the special series. The eliminating intraday trend series approach developed by Liu et al. is utilized to analyze the effects of power law decay change on correlation properties, and shuffling series originated by Viswanathan et al. for the impacts of special type of correlation on power‐law distribution.

It is found that the accelerating decay of power law has an insignificant effect on correlation properties of returns and the empirical results indicate that time scale may also be an important factor maintaining power law property of returns besides correlation. When time scale is under critical point, the effects of correlation are crucial, and the correlation of nonlinear long‐range presents the strongest influence. However, for time scale beyond critical point, the impact of correlation begins to diminish or even finally disappear and then the power law property shows complete dependence on time scale.

The 5‐min high frequency data of the Shanghai market as the empirical benchmark is insufficient to depict the relation over the entire time scale in the Chinese stock market.

The paper identifies the determinants of market dynamics to apply them to risk management through analysis of multi‐scale relations, and supports endeavors to introduce time parameter into further risk measures and control.

The paper provides the empirical evidence that time scale is one of the key determinants of market dynamics by analyzing the multi‐scale relation between power law distribution and correlation.

This paper develops visual aids for the understanding of two asset portfolio mathematics. Specifically, visual aids are utilized in teaching portfolio variance and correlation coefficient concepts. The presentation is simple, yet powerful, and is useful for an audience with varying levels of statistical sophistication. Consequently, the visual aids can replace or complement standard presentations of basic portfolio theory.

Refers to previous research on deciding the balance between equities and bonds in investment portfolios and puts forward a model based on a single period correlation to predict future stock‐bond correlations from past interest and growth rates. Explains the concepts involved and uses 1948‐2000 US data to test it. Shows that the model predicts stock‐bond correlation significantly better than the traditional method of extrapolating from past correlations; and relates this to the theory of loanable funds. Concludes that high interest rates and high growth lead to higher correlations between stocks and bonds and calls for further research.

This chapter investigates the correlation dynamics in the equity markets of 13 Asia-Pacific countries, Europe and the US using the asymmetric dynamic conditional correlation GARCH model (AG-DCC-GARCH) introduced by Cappiello, Engle, and Sheppard (2006). We find significant variation in correlation between markets through time. Stocks exhibit asymmetries in conditional correlations in addition to conditional volatility. Yet asymmetry is less apparent in less integrated markets. The Asian crisis acts as a structural break, with correlations increasing markedly between crisis countries during this period though the bear market in the early 2000s is a more significant event for correlations with developed markets. Our findings also provide further evidence consistent with increasing global market integration. The documented asymmetries and correlation dynamics have important implications for international portfolio diversification and asset allocation.

In this paper we develop a new semi-parametric model for conditional correlations, which combines parametric univariate Generalized Auto Regressive Conditional Heteroskedasticity specifications for the individual conditional volatilities with nonparametric kernel regression for the conditional correlations. This approach not only avoids the proliferation of parameters as the number of assets becomes large, which typically happens in conventional multivariate conditional volatility models, but also the rigid structure imposed by more parsimonious models, such as the dynamic conditional correlation model. An empirical application to the 30 Dow Jones stocks demonstrates that the model is able to capture interesting asymmetries in correlations and that it is competitive with standard parametric models in terms of constructing minimum variance portfolios and minimum tracking error portfolios.