Complex models have received significant interest in recent years and are being increasingly used to explain the stochastic phenomenon with upward and downward fluctuation such as the stock market. Different from existing semi-variance methods in traditional integer dimension construction for two variables, this paper proposes a simplified multi-factorized fractional dimension derivation with the exact Excel tool algorithm involving the fractional center moment extension to covariance, which is a complex parameter average that is a multi-factorized extension to Pearson covariance. By examining the peaks and troughs of gold price averages, the proposed algorithm provides more insight into revealing underlying stock market trends to see who is the financial market leader during good economic times. The calculation results demonstrate that the complex covariance is able to distinguish subtle differences among stock market performances and gold prices for the same field that the two variable covariance may overlook. We take London, Tokyo, Shanghai, Toronto, and Nasdaq as the representative examples.

中文翻译：

---

股市与黄金价格的多元半协方差

近年来，复杂的模型引起了人们的极大兴趣，并且越来越多地用于解释诸如股票市场之类的具有上下波动的随机现象。与传统的针对两个变量的整数维构造中的现有半方差方法不同，本文提出了一种精确的简化的多因子分数维推导方法，该方法采用精确的Excel工具算法，其中涉及分数中心矩扩展为协方差，这是一个复杂的参数平均值，即皮尔逊协方差的多因素扩展。通过检查黄金平均价格的波峰和波谷，所提出的算法可提供更多洞察力，揭示潜在的股票市场趋势，以了解谁在经济良好时期是金融市场的领导者。计算结果表明，复协方差能够区分两个变量协方差可能忽略的同一领域的股市表现和金价之间的细微差异。我们以伦敦，东京，上海，多伦多和纳斯达克为代表。