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

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