Abstract

We study the periodogram based estimate of spectral density of a strictly stationary random sequence and consider this estimate as a random function on the whole domain of frequency. We renormalize the scale in this domain and investigate the probability measure generated by obtained process in the space of continuous functions.

Keywords: Stationary time series, spectral density, periodogram based estimate, cumulant spectral densities, weak convergence.

MSC: 62M15, 60G10, 60G15

Pages:  31--37     

Volume  47 ,  Issue  1$-$2 ,  1995