Machine-Learning-Based Semiparametric Time Series Conditional Variance: Estimation and Forecasting

This paper proposes a new combined semiparametric estimator of the conditional variance that takes the product of a parametric estimator and a nonparametric estimator based on machine learning. A popular kernel-based machine learning algorithm, known as the kernel-regularized least squares estimator, is used to estimate the nonparametric component. We discuss how to estimate the semiparametric estimator using real data and how to use this estimator to make forecasts for the conditional variance. Simulations are conducted to show the dominance of the proposed estimator in terms of mean squared error. An empirical application using S&P 500 daily returns is analyzed, and the semiparametric estimator effectively forecasts future volatility.