The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Portmanteau Test Based on the Discrete Cosine Transform

이산코사인변환을 기반으로 한 포트맨토 검정

  • Oh, Sung-Un (Department of Statistics, Sookmyung Women's University) ;
  • Cho, Hye-Min (Department of Statistics, Sookmyung Women's University) ;
  • Yeo, In-Kwon (Department of Statistics, Sookmyung Women's University)
  • 오승언 (숙명여자대학교 통계학과) ;
  • 조혜민 (숙명여자대학교 통계학과) ;
  • 여인권 (숙명여자대학교 통계학과)
  • Published : 2007.07.31
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Abstract

We present a new type of portmanteau test in the frequency domain which is derived from the discrete cosine transform(DCT). For the stationary time series, DCT coefficients are asymptotically independent and their variances are expressed by linear combinations of autocovariances. The covariance matrix of DCT coefficients for white noises is diagonal matrix whose diagonal elements is the variance of time series. A simple way to test the independence of time series is that we divide DCT coefficients into two or three parts and then compare sample variances. We also do this by testing the slope in the linear regression model of which the response variables are absolute values or squares of coefficients. Simulation results show that the proposed tests has much higher powers than Ljung-Box test in most cases of our experiments.

이 논문에서는 이산코사인변환에 의해 유도된 주파수 공간상에서의 포트맨토검정법을 소개한다. 정상시계열의 경우 이산코사인변환 계수는 점근적으로 독립이고 분산은 자기공분산의 선형결합으로 표시된다. 백색잡음에 대한 이산코사인변환 계수의 공분산 행렬은 모든 대각원소가 시계열의 분산인 대각행렬이다. 시계열의 독립성을 검정하기 위해 계수들을 주파수 영역에 따라 2 또는 3개의 그룹으로 분할하고 그룹간의 분산을 비교하여 자료가 백색잡음인지 아닌지를 검정한다. 또한 계수의 제곱값이 반응변수이고 주파수 대역이 설명변수인 회귀모형에서 기울기를 검정하여 백색잡음 여부를 알아본다. 모의실험 결과를 보면 제안한 검정방법이 대부분의 경우 Ljung-Box 검정보다 높은 검정력을 가지는 것으로 나타났다.

Keywords

References

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