algorithm - 如何设计一种算法来查找多个变量的协方差？

Question

以下是两个变量ABC和XYZ的协方差方程。



下面是找到ABC和XYZ之间的协方差的算法。

Algorithm 1: Calculate Covariance
1. cov = 0
2. for i = 0 to size - 1
3.  cov = cov + (return_abc[i] - avg_abc) * (return_xyz[i] - avg_xyz)
4. end for
5. cov = cov / size - 1
6. end

如何设计一种算法来查找样本中一个变量与其余变量之间的协方差？
例如，如何找到APPLE的股票与纳斯达克的其余股票(约3,100家公司)之间的协方差？

Answer 1

http://www.investopedia.com/articles/financial-theory/11/calculating-covariance.asp

如果您仅查看日末价格(为简单起见)，并且希望将单个股票与其余所有股票进行比较，请尝试将其余全部视为一个元素，即:

n=number of days to analyze
marketReturn = average(return of each stock that isn't APPLE)
marketAverage = (sum of marketReturn's)/n
appleAverage = (sum of APPLE returns)/n

然后将总和应用于您要分析的天数的样本量。

Answer = (((day 1 APPLE return %)-(appleAverage))*((day 1 marketReturn %)-(marketAverage)) + ((day 2 APPLE return %)-(appleAverage))*((day 2 marketReturn %)-(marketAverage)) + ...)/(n-1)

我想如果您要单独检查每个库存:

for(x=0;x<numStocksNotAPPLE;++x)//increment through each stock
{
    covariantList[x]=(((day 1 APPLE return percent)-(appleAverage))*((day 1 stock[x] percent)-(stock[x] average)) + ... + (((day n APPLE return %)-(appleAverage))*((day n stock[x] %)-(stock[x] average)))/(n-1)
}//that should give you a covariant APPLE vs each stock

然后，如果只需要一个数字，则可以取covariantList的平均值:

foreach(covariantList c)
{
    sum+=c
}

averageCovariant = sum/covariantList.size

请记住，这都是伪代码，我并不是在声称任何功能都可以