Masani and Wiener asked to characterize the regularity of vector stationary stochastic processes. The question easily translates to a harmonic analysis question: for what matrix weights the Hilbert transform is bounded with respect to this weight? We solved this problem with Sergei Treil in 1996 introducing the matrix A_2 condition. But what is the sharp estimate of the Hilbert transform in terms of matrix A_2 norm is still unknown in a striking difference with scalar case. Convex body valued operators helped to get the estimate via norm in the power 3/2. But shouldn't it be power 1? We construct an example of a rather natural operator for which the estimate in scalar and vector case is indeed different. But it is neither the Hilbert transform, nor a sparse Lerner transform.