Hands-On Machine Learning for Algorithmic Trading

The assumptions made by PCA

PCA makes several assumptions that are important to keep in mind. These include the following:

• High variance implies a high signal-to-noise ratio
• The data is standardized so that the variance is comparable across features
• Linear transformations capture the relevant aspects of the data
• Higher-order statistics beyond the first and second moment do not matter, which implies that the data has a normal distribution

The emphasis on the first and second moments aligns with standard risk/return metrics, but the normality assumption may conflict with the characteristics of market data.