Asymptotic Properties of the Nonlinear Least Squares Estimator in HE-HAR Models

We examine the properties of nonlinear least squares (NLS) estimator for a nonlinear extension of the class of heterogeneous autoregressive (HAR) models for realized covariance (RC) matrices. The Monte Carlo (MC) experiments verify the asymptotic properties of the OLS for multivariate HAR specifications, used as a benchmark. Then we replicate the experiment to verify the same properties for the Hadamard exponential (HE)-based HAR extensions, establishing the convergence of regular HAR coefficients in all cases, while the asymptotic normality of the NLS estimates is uniquely confirmed for the “HE_vech-HAR” specification with log-transformed RC series. The only persistent but relatively narrow asymptotic bias is evident for the “HE” parameter estimate. We submit models in MC exercises to several sensitivity checks and show the robustness of corresponding results.