We propose a new estimator of high-dimensional spectral density matrices, called UNshrunk ALgebraic Spectral Estimator (UNALSE), under the assumption of an underlying low rank plus sparse structure, as typically assumed in dynamic factor models. The UNALSE is computed by minimizing a quadratic loss under a nuclear norm plus $l_1$ norm constraint to control the latent rank and the residual sparsity pattern. The loss function requires as input the classical smoothed periodogram estimator and two threshold parameters, the choice of which is thoroughly discussed. We prove consistency of UNALSE as both the dimension $p$ and the sample size $T$ diverge to infinity, as well as algebraic consistency, i.e., the recovery of latent rank and residual sparsity pattern with probability one. The finite sample properties of UNALSE are studied by means of an extended simulation exercise as well as an empirical analysis of US macroeconomic data.

翻译：我们提出一个新的高维光谱密度矩阵估计值,称为UNshrunk ALgebraic ALGERPERPERMATORSE(UNALSE),其假设是动态要素模型中通常假设的低等级加上稀疏结构。UNALSE的计算方法是在核规范下将二次损失降到最低,加上用于控制潜值和残余聚度模式的1美元标准限制值。损失功能要求将古典平滑时段测图仪和两个阈值参数作为输入,其选择经过透彻讨论。我们证明,UNALSE的维度是美元,样本大小为美元,与无限值相差,以及代数一致性,即以概率一恢复潜值和残余聚度模式。UNALSE的有限样本特性通过扩大模拟练习以及美国宏观经济数据的经验分析加以研究。