Michel Lubrano: michel.lubrano[at]univ-amu.fr
Pierre Michel: pierre.michel[at]univ-amu.fr
The least square estimator can be shown to depend only on a single parameter, the precision matrix. We show that a regularized estimate of the precision matrix can be directly used to obtain the least square solution even when the number of covariates can be strictly larger than the sample size. As biases can occur from different choices of the precision matrix estimate, we show how to construct a (nearly) unbiased estimator irrespectively of the sparsity within the data generating process. We call this estimator the Precision Least Squares (PrLS). Assuming stationarity for the covariates and the error process we show that the PrLS estimator is (i) asymptotically Gaussian, (ii) automatically free of the usual regularization bias and (iii) control the directional false discovery rate. As an application, we employ the Precision Least Squares to estimate the predictive connectedness among daily asset returns of 88 global banks. We show that financial crisis corresponds to a collapse of financial linkage in line with financial theory predictions.