Low-Rank Structured Nonparametric Prediction of Instantaneous Volatility

Based on It\^o semimartingale models, several studies have proposed methods for forecasting intraday volatility using high-frequency financial data. These approaches typically rely on restrictive parametric assumptions and are often vulnerable to model misspecification. To address this issue, we introduce a novel nonparametric prediction method for the future intraday instantaneous volatility process during trading hours, which leverages both previous days' data and the current day's observed intraday data. Our approach imposes an interday-by-intraday matrix representation of the instantaneous volatility, which is decomposed into a low-rank conditional expectation component and a noise matrix. To predict the future conditional expected volatility vector, we exploit this low-rank structure and propose the Structural Intraday-volatility Prediction (SIP) procedure. We establish the asymptotic properties of the SIP estimator and demonstrate its effectiveness through an out-of-sample prediction study using real high-frequency trading data.