# Principal component analysis

## Overview

The *Principle component analysis* (PCA) allows you to calculate a set of linearly uncorrelated series, or *components*, from a set of possibly correlated series. The component series are calculated using an orthogonal transform so that the first series captures the highest possible variance of the original set of series. Each successive series captures the highest possible remaining variance under the constraint that it is orthogonal to the preceding series.

The analysis also presents the eigenvectors and the eigenvalues.

## Settings

###### Do not include series used in calculations in the output

When checked, any series included in the calculation will be excluded from the output. Uncheck this setting if you want both the original series and the calculation result in the output.

###### Include new series automatically

When checked, any new series added to the input will automatically be included in the calculation.

###### Use correlation (normalize input)

The eigenvectors are calculated from the correlation matrix. This means that the input is centered and normalized before the components are calculated. PCA is sensitive to the scale of the input. Use this setting if variables are of different units, e.g. currencies or indices.

###### Use covariance

The eigenvectors are calculated from the covariance matrix. This means that the input is only centered before the components are calculated. PCA is sensitive to the scale of the input.

###### Number of components

The number of component series to calculate and include in the output. This number cannot be greater than the number of series included.

The components are in the order of how much variance of the original data set that they capture. If you select “Greatest” you will get the most significant series and with “Smallest” you will get the least significant series.

###### Output series description

Specify the description of the output series or use the default description.

###### Include

Select what series to include in the calculation.

## Output

There are three types of output.

###### Matrix

The matrix contains the eigenvectors of the correlation or covariance matrix. These vectors are orthonormal.

###### Category series

There are two category series: one with the eigenvalues and one with the cumulative proportion of the eigenvalues. The latter can be interpreted how much of the original variance that is captured by that principal component together with all preceding components.

###### Time series

The “Number of components” setting specifies how many component series that should be calculated. The series are either the most or least significant components.

The components are the eigenvectors projected in the time series space scaled so that the variance is the same as the corresponding eigenvalue.