Abbreviation: PCALagFilter
Category: Principal Components Analysis (PCA)
Input Parameters:
| Name | Range | Default |
| Time Series | Close | |
| Window Size | Int >= Max Lag + 1 | 50 |
| Threshold | Real >= 0.0 | 30 |
| Input Number | 1 <= Int <= Max Lag + 1 | 1 |
| Max Lag | Int >= 0 | 25 |
Calculation:
Performs the Principal Component Analysis of the last n points in the space of X, Lag(X,1), Lag (X,2), …, Lag(X,MaxLag), 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 Lag(X,m-1). 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
X = Time Series
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 Lag(X,m-1) filtered by removing all the other components. For more information on Principal Component Analysis refer to Principal Components Analysis (PCA) Discussion.