Sample cross-correlations for moving averages with regularly varying tails (Q2744936)

A pair of moving average processes \(x^{(i)}_t=\sum_{j=0}^\infty c^{(i)}_jz^{(i)}_{t-j}\), \(i=1,2\), is considered, where \(c^{(i)}_j\) are fixed numbers, \((z^{(1)}_j,z^{(2)}_j)\) are i.i.d. vectors with distribution \(\mu\). It is supposed that \(\mu\) varies regularly with exponent \(E=\text{diag}(a_1,a_2)\), i.e., there exists a matrix sequence \(A_n\) such that \(n\mu(A^{-1}_n dx)\) converges vaguely to some finite measure and \(A_{[n\lambda]}A^{-1}_n\to\exp(-E\log\lambda)\) for any \(\lambda>0\). For such processes the authors investigate the asymptotic behaviour of centered normalized convenient sample cross-covariances and sample cross-correlations.