Enhancing stock price data analysis through variants of principal component analysis

Abstract

This work investigates and identifies suitable dimensionality reduction approaches based on variants of principal component analysis (PCA) for various transformations of stock price data. The classical PCA, dynamic principal component analysis (DPCA) and generalised dynamic principal component analysis (GDPCA) were applied to the closing prices, simple returns and log of returns of the top 100 holdings of Standard & Poor’s 500 (S&P500) from year 2020 to year 2023. The S&P 500 is a stock market index that tracks the stock performance of 500 large-cap U.S. companies. The performances of the aforementioned variants of PCA on these data for different timeframes were compared. Results showed that GDPCA works best for non-stationary time series data such as the closing prices and DPCA works best for stationary time series data such as the simple returns and the log of returns. The results obtained from the empirical analysis was further supported by simulation studies that follow, hence GDPCA and DPCA could be among the most appropriate dimensionality reduction approaches for non-stationary and stationary time series data respectively.