A Whiteness Test Based On The Spectral Measure Of Large Non-Hermitian Random Matrices

In the context of multivariate time series, a whiteness test against an MA(1) correlation model is proposed. This test is built on the eigenvalue distribution (spectral measure) of the non-Hermitian one-lag sample autocovariance matrix, instead of its singular value distribution. The large dimensional limit spectral measure of this matrix is derived. To obtain this result, a control over the smallest singular value of a related random matrix is provided. Numerical simulations show the excellent performance of this test.