  In this paper, we propose a novel high-dimensional time-varying coefficient
estimator for noisy high-frequency observations. In high-frequency finance, we
often observe that noises dominate a signal of an underlying true process.
Thus, we cannot apply usual regression procedures to analyze noisy
high-frequency observations. To handle this issue, we first employ a smoothing
method for the observed variables. However, the smoothed variables still
contain non-negligible noises. To manage these non-negligible noises and the
high dimensionality, we propose a nonconvex penalized regression method for
each local coefficient. This method produces consistent but biased local
coefficient estimators. To estimate the integrated coefficients, we propose a
debiasing scheme and obtain a debiased integrated coefficient estimator using
debiased local coefficient estimators. Then, to further account for the
sparsity structure of the coefficients, we apply a thresholding scheme to the
debiased integrated coefficient estimator. We call this scheme the Thresholded
dEbiased Nonconvex LASSO (TEN-LASSO) estimator. Furthermore, this paper
establishes the concentration properties of the TEN-LASSO estimator and
discusses a nonconvex optimization algorithm.
