In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite $4+\varepsilon$, $\varepsilon>0$, moments. Also, the population covariance matrix with unbounded spectrum can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S\&P 500 index.

翻译：在本文中,随机矩阵理论得出了随机矩阵理论的新结果,使我们能够在缩小目标是一个随机对象时,对全球最低差异组合进行缩略估计。更具体地说,缩小目标被确定为根据以往数据估计的持有量组合。理论调查结果用于为动态估计全球最低差异组合制定理论,在每次重建时,其重量的新估算者缩到持有量组合,其重量的新估算者在每次重建时,其重量缩到持有量组合中。在有样本和没有样本重叠的两种情况下,都在文件中加以考虑。非重叠抽样与资产回报的不同数据用于建立传统全球最低差异组合加权数和确定目标组合的情况相对应,而重叠案件则允许样本之间的交叉。理论结果来自数据生成过程的薄弱假设。除了假设有一定的4 ⁇ varepslon$, $\varepslon>0, 片段。此外,可以考虑使用非宽频谱的人口差异矩阵来构建资产回报表,用于构建传统对资产回报组合进行评估,确定目标组合,而重叠案件则允许在样本中进行交叉选择。根据广泛模拟对500号进行新的交易战略的绩效进行了研究。最后通过S-provical 进行模拟,对500号进行了分析。