Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor

In this article, we propose a computationally efficient approach to estimate (large) pp-dimensional covariance matrices of ordered (or longitudinal) data based on an independent sample of size nn. To do this, we construct the estimator based on a kk-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerably faster than many existing methods and only requires inversion of (k+1)(k+1)-dimensional covariance matrices. The resulting estimator is positive definite as long as k