On the limiting spectral distribution of sample autocovariance matrix of (Non)linear time series

We derive spectral distribution results for a large class of time series model, including multivariate linear and nonlinear time series. Under a classical setting that the number of observations n increased, the dimension p also increased and the ratio  p/n  tends to a positive constant,  we present that limiting spectral distribution (LSD) of the sample autocovariance matrix concentrates to its expectation. Furthermore, the LSD of the sample covariance matrix also concentrates to the LSD of the sample covariance matrix of a Gaussian process with the same covariance as the original process. With some further assumptions to the processes, the limiting spectral distribution exists and the limiting moments can be calculated.