0000000000769040
AUTHOR
Rainer Dahlhaus
ON THE ASYMPTOTIC DISTRIBUTION OF BARTLETT'S Up-STATISTIC
Abstract. In this paper the asymptotic behaviour of Bartlett's Up-statistic for a goodness-of-fit test for stationary processes, is considered. The asymptotic distribution of the test process is given under the assumption that a central limit theorem for the empirical spectral distribution function holds. It is shown that the Up-statistic tends to the supremum of a tied down Brownian motion. By a counterexample we refute the conjecture that this distribution is in general of the Kolmogorov-Smirnov type. The validity of the central limit theorem for the spectral distribution function is then discussed. Finally a goodness-of-fit test for ARMA-processes based on the estimated innovation sequen…
SPECTRAL ANALYSIS WITH TAPERED DATA
. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.