On singular value distribution of large-dimensional autocovariance matrices

On singular value distribution of large-dimensional autocovariance matrices

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

Discussion of “ High - dimensional autocovariance matrices and optimal linear prediction ” ∗ , †

First, we would like to congratulate Prof. McMurry and Prof. Politis for their thought-provoking paper on the optimal linear prediction based on full time series sample (hereafter, referred as [MP15]). [MP15] considered the one-step optimal linear predictor X∗ n+1 = ∑n i=1 φi(n)Xn+1−i of a univariate time series X1, . . . , Xn in the ` 2 sense which is given by the solution of the Yule-Walker e...

An Approximate Singular Value Decomposition of Large Matrices in Julia

In this project, I implement a parallel approximate singular value decomposition (SVD) in Julia. The approach taken here follows the algorithm described by Friedland et al., [1] and implement it using AbstractMatrices and DArrays in Julia to give the user additional flexibility. For additional speed, the algorithm makes direct calls to the DGEMV routine in the BLAS kernels. An error analysis us...

High-dimensional autocovariance matrices and optimal linear prediction

A new methodology for optimal linear prediction of a stationary time series is introduced. Given a sample X1, . . . , Xn, the optimal linear predictor of Xn+1 is X̃n+1 = φ1(n)Xn + φ2(n)Xn−1 + . . .+φn(n)X1. In practice, the coefficient vector φ(n) ≡ (φ1(n), φ2(n), . . . , φn(n)) is routinely truncated to its first p components in order to be consistently estimated. By contrast, we employ a consi...