Fuzzy Correlation Measurement Algorithms for Big Data and Application to Exchange Rates and Stock Prices

In the era of Internet of people and things, big data are merging. Conventional computation algorithms including correlation measures become inefficient to deal with big data problems. Motivated by this observation, we present three fuzzy correlation measurement algorithms, that is, the centroid-based measure, the integral-based measure, and the α-cut-based measure using fuzzy techniques. Data of Shanghai stock price index (SSI) and exchange rates of main foreign currencies over China Yuan from 22 January 2013 to 17 May 2018 are used to check the effectiveness of our algorithms, and, more importantly, to observe the causality relationship between SSI and these main exchange rates. We have observed some findings as follows. First, the usage of the highest, lowest, or closing values in daily exchange rates and stock prices has impact on the significant Granger causes of exchange rates over SSI, but does not produce any opposite cause from SSI to exchange rates. Second, no matter which of our fuzzy measurement algorithms is used, Hongkong Dollar over China Yuan and U.S. Dollar over China Yuan are positively related with SSI, and Euro over China Yuan negatively correlated with SSI is always recognized as a Granger cause to SSI with the significance level being 1%. Finally, both the optimism level and the uncertainty level are observed having impact on the correlation coefficients, but the later brings more significant changes to results of the Granger causality tests.