The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Re-Transformation of Power Transformation for ARMA(p, q) Model - Simulation Study

ARMA(p, q) 모형에서 멱변환의 재변환에 관한 연구 - 모의실험을 중심으로

  • Kang, Jun-Hoon (Department of Statistics, Hankuk University of Foreign Studies) ;
  • Shin, Key-Il (Department of Statistics, Hankuk University of Foreign Studies)
  • 강전훈 (한국외국어대학교 통계학과) ;
  • 신기일 (한국외국어대학교 통계학과)
  • Received : 2015.03.20
  • Accepted : 2015.05.26
  • Published : 2015.06.30
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Abstract

For time series analysis, power transformation (especially log-transformation) is widely used for variance stabilization or normalization for stationary ARMA(p, q) model. A simple and naive back transformed forecast is obtained by taking the inverse function of expectation. However, this back transformed forecast has a bias. Under the assumption that the log-transformed data is normally distributed. The unbiased back transformed forecast can be obtained by the expectation of log-normal distribution; consequently, the property of this back transformation was studied by Granger and Newbold (1976). We investigate the sensitivity of back transformed forecasts under several different underlying distributions using simulation studies.

ARMA(p, q) 모형 분석에서 분산 안정화 또는 정규화를 위해 멱변환(power transformation)이 사용된다. 변환된 자료를 이용하여 분석이 이루어지며 원 자료의 예측을 위해 재변환이 사용된다. 이때 흔히 변환된 자료 분석에서 얻어진 예측값의 역함수 값이 원자료 예측값으로 사용되지만 이는 편향이 있는 것으로 알려져 있다. 이를 해결하기 위해 로그 변환의 경우 Granger과 Newbold (1976)는 로그-정규분포의 기댓값을 이용할 것을 제안하였다. 본 연구에서는 모의실험을 통하여 제곱근 변환과 로그 변환 후 재변환을 사용할 때 예측값으로 기댓값의 역함수를 이용하는 방법과 역함수의 기댓값을 사용하였을 때의 추정의 결과를 모의실험을 통하여 비교하였다.

Keywords

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