# 10-Dimensional PCA Filtering (Professional Only)

Abbreviation: PCA10Filter
Category: Principal Components Analysis (PCA)
Input Parameters:

 Name Range Default Time Series #1 Close Time Series #2 Close Time Series #3 Close Time Series #4 Close Time Series #5 Close Time Series #6 Close Time Series #7 Close Time Series #8 Close Time Series #9 Close Time Series #10 Close Window Size Int >= 10 50 Threshold Real >= 0.0 30 Input Number 1 <= Int <= 10 1

Calculation:

Performs the Principal Component Analysis of the last n points in the space of X1…X10, calculates all eigenvectors and eigenvalues. Calculates the projection of the latest time point to the direction determined by several first eigenvectors, and returns its mth component (filtered value of Xm). The number of eigenvectors taken into account is determined by the demand that the sum of eigenvalues of these eigenvectors is as small as possible provided that it is not less that p% of the sum of all eigenvalues. (Each eigenvalue is less than or equal to the preceding eigenvalue.)

where

X1 = Time Series 1
X2 = Time Series 2
X3 = Time Series 3
X4 = Time Series 4
X5 = Time Series 5
X6 = Time Series 6
X7 = Time Series 7
X8 = Time Series 8
X9 = Time Series 9
X10 = Time Series 10
n = Window Size
p = Threshold
m = Input Number

Discussion:

Sums up several first principal components that provide together not less than p % of the total variance. Returns the value of Xm filtered by removing all the other components. For more information on Principal Component Analysis refer to Principal Components Analysis (PCA) Discussion.