Comparison And Application Of Several Correlation Analysis Methods

Correlation analysis involves various fields of human activities,including natural science,social life,financial markets,medical research,etc.,and has been a research hotspot for data exploration.In the current era of big data,the huge amount of data and the diversity of features have brought challenges about correlation analysis,but also provided us with the opportunity to discover correlations between non-intuitive variables.In this paper,we consider the advantages and disadvantages of the correlation analysis methods from three aspects,explore suitable analysis methods and mine the nonlinear correlation between variables.We want to fully characterize the correlation between variables and explain its transmission mechanism in a reasonable way,and conduct an empirical analysis on the data of the US dollar index and its possible influencing factors.Firstly,we integrated the economic situation of the Trade disputes between China and the United States,selected two variables,the US dollar index and the RMB exchange rate,and calculated the statistical correlation coefficient value to explore the correlation between them.The research results found that the statistical correlation coefficient between the US dollar index and the RMB exchange rate was about 0.538,while the auto-correlation coefficient of the US dollar index did not exceed 0.150,and the correlation degree after the Trade disputes was greater than before.This shows that the correlation exists,but the linear correlation is not high,and the statistical correlation coefficient only depends on the linear model and does not completely describe the correlation between the variables.Secondly,in order to explore other correlations between the US dollar index and the RMB exchange rate,we calculates its probability correlation coefficient,and the comparison results show that the probability of the same direction is about 0.705,which is greater than the calculation result of statistical correlation;there are obvious differences between the probability autocorrelation and statistical autocorrelation,not only in the numerical value,but also in the positive and negative directions.Through quantitative calculations,we consider that the statistical correlation coefficient only characterizes the linear correlation,but the probability correlation coefficient can characterize its non-linear correlation.The correlation between the US dollar index and the RMB exchange rate after the Trade disputes is greater than before,and the influence of this relationship is mainly reflected in the linear correlation.However,neither the statistical correlation coefficient nor the probability correlation coefficient can explain the transmission mechanism of the correlation between the US dollar index and the RMB exchange rate.Finally,in order to solve the transmission mechanism problem,we establish a path correlation model and extend it to a path indirect correlation model.Since each exchange rate in the calculation formula of the US dollar index corresponds to a constant coefficient,considering that the exchange rate changes in real time,the path correlation model established in this paper fits these constant coefficients with a non-linear model to design time-varying coefficients and errors,to reflect the changes in the real data.By adding a single or multiple variables to the non-linear part,the direct and indirect correlations between the linear and non-linear variables and the dependent variables are analyzed from different time perspectives.The research results found that the path correlation model can explain the transmission mechanism of linear correlation and non-linear correlation between multiple variables and each variable.