PCA and FA Intro

Difference between PCA and FA to Others

Recall:

Multiple Regression (MR): relationship between an exogenous variable and many endogenous variable

Cointegration: endogenous variables are stationary (means the joint probability distribution does not shift through time and space, mean and variance remain constant throughout time and position)

Mean-Variance Analysis: measures the total collective variability of a group of variables, without specifically identifying which subgroups contribute to that variability

PCA and FA

• compared to MR examines only the endogenous variables
• compared to Cointegration it may not need to be stationary
• compared to Mean-Variance Analysis, PCA identify and rank subgroups and their contribution to the total variability
• Both uses variance-covariance matrix

Characteristics of Mutivariate Statistics

• Volatility in the multivariate structure
• Correlation or colinearity between variables

Principal Components Analysis

- volatility of multivariate structure is measured and analyzed

- total variability is measured by the sum of the eigenvalues (sum of the diagonals in the matrix)

Factor Analysis

- correlation between the variables of  a multivariate structure is analyzed

Sources: Quantitative Methods in Finance by Watsham and Parramore