# 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, $$L_2-norm; and; L{\infty}-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0N^{-r} both in the pointwiseand$$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.

#### References

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