Forecasting High-Dimensional Covariance Matrices Using High-Dimensional Principal Component Analysis

Abstract

We modify the recently proposed forecasting model of high-dimensional covariance matrices (HDCM) of asset returns using high-dimensional principal component analysis (PCA). It is well-known that when the sample size is smaller than the dimension, eigenvalues estimated by classical PCA have a bias. In particular, a very small number of eigenvalues are extremely large and they are called spiked eigenvalues. High-dimensional PCA gives eigenvalues which correct the biases of the spiked eigenvalues. This situation also happens in the financial field, especially in situations where high-frequency and high-dimensional data are handled. The research aims to estimate the HDCM of asset returns using high-dimensional PCA for the realized covariance matrix using the Nikkei 225 data, it estimates 5- and 10-min intraday asset-returns intervals. We construct time-series models for eigenvalues which are estimated by each PCA, and forecast HDCM. Our simulation analysis shows that the high-dimensional PCA has better estimation performance than classical PCA for the estimating integrated covariance matrix. In our empirical analysis, we show that we will be able to improve the forecasting performance using the high-dimensional PCA and make a portfolio with smaller variance.