Convergence Properties of a Spectral Density Estimator

  • Gyeong Hye Shin (Lecturer, Department of mathematics, Yonsei University, Seoul, 120-749, Korea) ;
  • Hae Kyung Kim (Professor, Department of mathematics, Yonsei University, Seoul, 120-749, Korea)
  • Published : 1996.12.01

Abstract

this paper deal with the estimation of the power spectral density function of time series. A kernel estimator which is based on local average is defined and the rates of convergence of the pointwise, $$L_2$-norm; and; $L{\infty}$-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0$N^{-r}$ both in the pointwiseand $$L_2$-norm, while; $N^{r-1}(logN)^{-r}$is the optimal rate in the $L{\infty}-norm$. Some examples are given to illustrate the application of main results.

Keywords

References

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