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http://dx.doi.org/10.5351/KJAS.2015.28.3.511

Re-Transformation of Power Transformation for ARMA(p, q) Model - Simulation Study  

Kang, Jun-Hoon (Department of Statistics, Hankuk University of Foreign Studies)
Shin, Key-Il (Department of Statistics, Hankuk University of Foreign Studies)
Publication Information
The Korean Journal of Applied Statistics / v.28, no.3, 2015 , pp. 511-527 More about this Journal
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.
Keywords
power transformation; moment; stationary time series; power-normal distribution;
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Andrews, P. E. and Herzberg, A. M. (1985). The Data: A Collection of Problems from Statistics, Springer-Verlag, Berlin.
2 Box, G. E. P. and Cox, D. R. (1964). An analysis of transformation, Journal of the Royal Statistical Society, Series, B, 26, 211-252.
3 Freeman, J. and Modarres, R. (2006). Inverse Box-Cox: The power-normal distribution, Statistics & Probability Letters, 76, 764-772.   DOI   ScienceOn
4 Granger, C. W. J. and Newbold, P. (1976). Forecasting transformed series, Journal of the Royal Statistical Society, Series, B, 38, 189-203.
5 Ha, M. H. and Kim, S. (2008). Internet traffic forecasting using power transformation heteroscadastic time series models, The Korean Journal of Applied Statistics, 21, 1037-1044.   DOI   ScienceOn
6 Helmut, L. and Fang, X. (2012). The role of the log transformation in forecasting economic variables, Empir Econ, 42, 619-638.   DOI
7 Hur, N.-K., Jung, J.-Y., Kim, S. (2009). A Study on air demand forecasting using multivariate time series models, The Korean Journal of Applied Statistics, 22, 1007-1017.   DOI   ScienceOn
8 Kim, S. and Seong, B. (2011). Intervention analysis of Korea tourism data, The Korean Journal of Applied Statistics, 24, 735-743.   DOI   ScienceOn
9 Lee, J.-S., Sohn, H. G. and Kim, S. (2013). Daily peak load forecasting for electricity demand by time series models, The Korean Journal of Applied Statistics, 26, 349-360.   DOI   ScienceOn
10 Nicholson, D. F. (1950). Population oscillations caused by competition for food, Nature, London, 165, 476-477.   DOI
11 Tong, H. (1983). Threshold Models in Non-Linear Time Series Analysis, Springer-verlag, Berlin.
12 Wei, W. W. S. (1990). Time Series Analysis : Univariate and Multivariate Methods, Pearson.
13 Yeo, I. and Johnson, R. A. (2000). A new family of power transformation to improve normality or symmetry, Biometrika, 87, 954-959.   DOI   ScienceOn