Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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JOINT ASYMPTOTIC DISTRIBUTIONS OF SAMPLE AUTOCORRELATIONS FOR TIME SERIES OF MARTINGALE DIFFERENCES

  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University) ;
  • Baek, J.S. (Department of Statistics, Sookmyung Women's University) ;
  • Lim, K.E. (Department of Statistics, Sookmyung Women's University)
  • Published : 2006.12.31
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Abstract

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.

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References

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