Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Asymptotics in Transformed ARMA Models

  • Yeo, In-Kwon (Department of Statistics, Sookmyung Women's University)
  • Received : 20100800
  • Accepted : 20101100
  • Published : 2011.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, asymptotic results are investigated when a parametric transformation is applied to ARMA models. The conditions are determined to ensure the strong consistency and the asymptotic normality of maximum likelihood estimators and the correct coverage probability of the forecast interval obtained by the transformation and backtransformation approach.

Keywords

References

  1. Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations, Journal of the Royal Statistical Society, Series. B, 26, 211-252.
  2. Burbidge, J. B., Magee, L. and Robb, A. L. (1988). Alternative transformations to handle extreme values of the dependent variable, Journal of the American Statistical Association. 83, 123-127. https://doi.org/10.2307/2288929
  3. Cho, H., Oh, S. and Yeo, I. K. (2007). Prediction interval estimation in transformed ARMA models, The Korean Journal of Applied Statistics. 20, 541–550.
  4. Cho, K. Yeo, I., Johnson, R. A. and Loh, W. Y. (2001a). Asymptotic theory for Box-Cox transformation in linear models, Statistics and Probability Letters, 51, 337–343.
  5. Cho, K. Yeo, I., Johnson, R. A. and Loh, W. Y. (2001b). Prediction interval estimation in transformed linear models , Statistics and Probability Letters, 51, 345-350. https://doi.org/10.1016/S0167-7152(00)00169-3
  6. Dunsmuir, W. (1983). A central limit theorem for estimation in Gaussian stationary time series observed at unequally spaced times, Stochastic Processes and Their Applications, 14, 279-295. https://doi.org/10.1016/0304-4149(83)90005-4
  7. Fama, E. F. (1965). The behavior of stock market prices, Journal of Business, 38, 34-105. https://doi.org/10.1086/294743
  8. John, J. A. and Draper, N. R. (1980). An alternative family of transformations, Applied Statistics, 29, 190-197. https://doi.org/10.2307/2986305
  9. Kosmala, W. A. J. (1995). Introductory Mathematical Analysis, William C Brown Publishers.
  10. Li, D. (1999). Value at Risk Based on the Volatility Skewness and Kurtosis, RiskMetrics Working Paper.
  11. McCulloch, J. H. (1996). Financial applications of stable distribution, Handbook of Statistics, 14, 393-425. https://doi.org/10.1016/S0169-7161(96)14015-3
  12. McDonald, J. B. (1996). Probability distribution for financial models, Handbook of Statistics, 14, 427-461. https://doi.org/10.1016/S0169-7161(96)14016-5
  13. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrika, 59, 347-370. https://doi.org/10.2307/2938260
  14. Rubin, H. (1956). Uniform convergence of random functions with applications to statistics, Annals of Mathematical Statistics, 27, 200–203.
  15. Yeo, I. K. and Johnson, R. A. (2000). A new family of power transformations to improve normality or symmetry, Biometrika, 87, 954-959. https://doi.org/10.1093/biomet/87.4.954