Using Eigenstructure and Factor Analysis to Explore Financial Data

Summary

This article introduces eigenvalues and eigenvectors as tools for examining relationships among measured variables. It distinguishes principal component analysis, which forms orthogonal components that capture variance, from factor analysis, which models observed variables as influenced by latent factors. Factor loadings are derived from eigenvectors scaled by the square roots of their eigenvalues, helping identify which variables may share underlying influences. The article also describes the Kaiser-Meyer-Olkin measure and Bartlett’s test as checks on whether a dataset may be suitable for factor analysis.

An MQL5 example applies these ideas to financial indicators, including moving averages and ATR values at multiple window lengths, using daily Bitcoin data over a stated historical period. The article further explores eigenstructure across time and reports that coherence between selected crypto assets varies, with higher windows showing some periods of stability and near-zero coherence. These are exploratory observations, not evidence of a tradable edge. Results depend on the selected variables, sampling period, and implementation; factor interpretations and time-varying relationships require careful validation.

Key ideas

• Eigenvectors give directions of variation in a correlation matrix, while eigenvalues indicate the associated variance.
• PCA summarizes variance with orthogonal components, whereas factor analysis seeks latent drivers of observed variables.
• Factor loadings connect observed variables to candidate factors and can help assess how many factors are useful.
• KMO and Bartlett’s test are presented as diagnostics for factor-analysis suitability.
• The examples explore indicator relationships and changing coherence across crypto assets without establishing a profitable strategy.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.