• Journal of the Korean Statistical Society
• /
• v.35 no.4
• /
• pp.453-458
• /
• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• The Korean Journal of Applied Statistics
• /
• v.21 no.5
• /
• pp.783-789
• /
• 2008

We investigate the effects of the misspecification of cointegrating(CI) ranks at other frequencies on the inference of seasonal models at the frequency of interest; our study includes tests for CI ranks and estimation of CI vectors. Earlier studies focused mostly on a single frequency corresponding to one seasonal root at a time, ignoring possible cointegration at the remaining frequencies. We investigate the effects of the mis-specification, especially in finite samples, by adopting Gaussian reduced rank(GRR) estimation by Ahn and Reinsel (1994) that considers cointegration at all frequencies of seasonal unit roots simultaneously. It is observed that the identification of the seasonal CI rank at the frequency of interest is sensitive to the mis-prespecification of the CI ranks at other frequencies, mainly when the CI ranks at the remaining frequencies are underspecified.