Note on the autoregressive spectral estimator

Abstract

An estimator of the spectral density of a stationary time series is obtained by fitting to the observations an autoregressive model (often including the estimation of its order), and computing with sample values the spectrum of the indicated model. In the present note we consider the calculation of simultaneous confidence bands, according to Newton and Pagano (1984). The procedure is illustrated by means of Monte Carlo simulations, for series generated by autoregressive models or orders up to 5. Key words and phrases. Confidence bands, asymptotic properties, Monte Carlo, Estimation of autoregressive order