Barlett’s Formula for Non Linear Processes

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations ofnonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as thesum of two terms. The first term corresponds to the standard Bartlett’s formula for linear processes,involving only the autocorrelation function of the observed process. The second term, which is specificto nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of thelinear innovation process and the autocorrelation function of its square. This formula is obtained under asymmetry assumption on the linear innovation process. An application to GARCH models is proposed.