A0186
Title: Nonconvex high-dimensional time-varying coefficient estimation for noisy high-frequency observations
Authors: Minseok Shin - KAIST (Korea, South) [presenting]
Donggyu Kim - KAIST (Korea, South)
Abstract: A novel high-dimensional time-varying coefficient estimator is proposed for noisy high-frequency observations. In high-frequency finance, it is often observed that noises dominate a signal of an underlying true process. Thus, usual regression procedures cannot be applied to analyze noisy high-frequency observations. To handle this issue, a smoothing method is first employed for the observed variables. However, the smoothed variables still contain non-negligible noises. To manage these non-negligible noises and the high dimensionality, a nonconvex penalized regression method is proposed for each local coefficient. This method produces consistent but biased local coefficient estimators. A debiasing scheme is proposed to estimate the integrated coefficients, and a debiased integrated coefficient estimator is obtained using debiased local coefficient estimators. Then, to further account for the sparsity structure of the coefficients, a thresholding scheme is applied to the debiased integrated coefficient estimator. This scheme is called the thresholded debiased nonconvex lasso (TEN-LASSO) estimator. Furthermore, the concentration properties of the TEN-LASSO estimator are established, and a nonconvex optimization algorithm is discussed.
