The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation for random coefficient autoregressive model

확률계수 자기회귀 모형의 추정

  • Kim, Ju Sung (Department of Information and Statistics, Chungbuk National University) ;
  • Lee, Sung Duck (Department of Information and Statistics, Chungbuk National University) ;
  • Jo, Na Rae (Department of Information and Statistics, Chungbuk National University) ;
  • Ham, In Suk (Department of Nursing Science, Chungbuk National University)
  • Received : 2015.12.31
  • Accepted : 2016.01.03
  • Published : 2016.02.29
Download PDF
⟨ Previous Next ⟩

Abstract

Random Coefficient Autoregressive models (RCA) have attracted increased interest due to the wide range of applications in biology, economics, meteorology and finance. We consider an RCA as an appropriate model for non-linear properties and better than an AR model for linear properties. We study the methods of RCA parameter estimation. Especially we proposed the special case that an random coefficient ${\phi}(t)$ has the initial value ${\phi}(0)$ in the RCA model. In practical study, we estimated the parameters and compared Prediction Error Sum of Squares (PRESS) criterion between AR and RCA using Korean Mumps data.

비선형 모형인 확률계수 자기회귀 모형의 모수를 추정하기 위해 전체 데이터를 부표본으로 나누어 확률계수 ${\phi}(t)$가 초기값, ${\phi}(0)$를 갖는 특별한 경우를 제안하고 추정하였다. 모의 실험으로 부표본으로 나누어 확률계수 자기회귀 모형을 추정하는 더 바람직함을 확인하였다. 실증분석에서는 한국 Mumps 자료를 선형 모형인 자기회귀 모형과 확률 계수 자기회귀 모형에 각각 적합시켜 모수를 추정하고, PRESS 값을 비교하여 확률계수 자기회귀 모형의 예측이 더 우수함을 보였다.

Keywords

References

  1. Aue, A., Horvath, L., and Steinebach, J. (2004). Estimation in random coefficient autoregressive models, Journal of Time Series Analysis, 27, 61-76.
  2. Hwang, S. Y. and Basawa, I. V. (1998). Parameter estimation for generalized random coefficient autoregressive processes, Journal of Statistical Planning and Inference, 68, 323-337. https://doi.org/10.1016/S0378-3758(97)00147-X
  3. Nicholls, D. F. and Quinn, B. G. (1981). The estimation of random coefficient autoregressive models II, Journal of Time Series Analysis, 2, 185-203. https://doi.org/10.1111/j.1467-9892.1981.tb00321.x
  4. Norli, A. A., Ibrahim, M., Shelton, P., and Nor, A. A. (2011). A new iterative procedure for estimation of RCA parameters based on estimating functions, Mathmatical Sciences, 5, 193-202.
  5. Rahiala, M. (1999). Random coefficient auto regressive model for longitudinal data, Biometrika, 86, 718-722. https://doi.org/10.1093/biomet/86.3.718
  6. Son, Y. S. (1996). Estimation of random coefficient AR(1) model for panel data, Journal of the Korean Statistical Society, 25, 529-544.
  7. Tong, H. (1990). Non-Linear Time Series, Oxford University Press, Oxford.
  8. Wang, D. and Ghosh, S. K. (2002). Bayesian analysis of random coefficient autoregressive models, Model Assisted Statistics and Applications, 3, 281-295.