The HAR model dominates current volatility forecasting. This model implies a restricted lag approach, with three parameters accounting for an AR(22) structure. This paper uses the Lasso method, which selects a parsimonious lag structure, while allowing both a flexible lag structure and lags...

We study the estimation of the high-dimensional covariance matrix and its eigenvalues under dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We first investigate the empirical spectral distribution (ESD) of the sample covariance...

We establish a framework to study the factor structure in stock variance under a high-frequency and high-dimensional setup. We prove the consistency of conducting principal component analysis on realized variances in estimating the factor structure. Moreover, based on strong empirical evidence,...

The long-memory and nonlinearity coexist in realised volatility. This paper incorporates the linear AR and HAR models with regime-switching models, including the smooth transition and Markov-switching approaches, to assess the forecasting performance of realized volatility. In-sample results...