Does the Box-Cox transformation help in forecasting macroeconomic time series?

International Journal of Forecasting

Volumn 29, Issue 1, 2013, Pages 88-99

  Proietti, Tommaso ^a,b   Lütkepohl, Helmut ^c,d  

^a UNIVERSITY OF SYDNEY   (Australia)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

^d DIW BERLIN   (Germany)

Author keywords

Forecast comparisons; Multi step forecasting; Nonparametric estimation of prediction error variance; Rolling forecasts

Indexed keywords

EID: 84865583025     PISSN: 01692070     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijforecast.2012.06.001     Document Type: Article

References (46)

1. Abadir K.M. An introduction to hypergeometric functions for economists. Econometric Reviews 1999, 18:287-330.
2. Handbook of mathematical functions 1964, Dover Publications, NY. M. Abramowitz, I.A. Stegun (Eds.).
3. Amemiya T. Advanced econometrics 1985, Basil Blackwell, Oxford, UK.
4. Atkinson A.C. Testing transformations to normality. Journal of the Royal Statistical Society, Series B 1973, 35:473-479.
5. Bårdsen G., Lütkepohl H. Forecasting levels of log variables in vector autoregressions. International Journal of Forecasting 2011, 27:1108-1115.
6. Box G.E.P., Cox D.R. An analysis of transformations (with discussion). Journal of the Royal Statistical Society, Series B 1964, 26:211-246.
7. Box G.E.P., Jenkins G.M. Time series analysis: forecasting and control 1970, Holden-Day, San Francisco.
8. Box G.E.P., Jenkins G.M. Some comments on a paper by Chatfield and Prothero and on a review by Kendall. Journal of the Royal Statistical Society, Series A 1973, 136:337-352.
9. Brockwell P.J., Davis R.A. Time series: theory and methods 1991, Springer-Verlag, New York.
10. Cameron M.A. The prediction variance and related statistics for stationary time series. Biometrika 1978, 65:283-296.
11. Carroll R.J., Ruppert D. On prediction and the power transformation family. Biometrika 1981, 68:609-615.
12. Chatfield C., Prothero D.L. Box-Jenkins seasonal forecasting: problems in a case-study. Journal of the Royal Statistical Society, Series A 1973, 136:295-315.
13. Clements M.P., Hendry D.F. An empirical study of seasonal unit roots in forecasting. International Journal of Forecasting 1997, 13:341-355.
14. Cleveland W.S., Devlin S.J. Calendar effects in monthly time series: detection by spectrum analysis and graphical methods. Journal of the American Statistical Association 1980, 75:487-496.
15. Cleveland W.S., Devlin S.J. Calendar effects in monthly time series: modeling and adjustment. Journal of the American Statistical Association 1982, 77:520-528.
16. Collins S. Prediction techniques for Box-Cox regression models. Journal of Business and Economic Statistics 1991, 9:267-277.
17. Davis H.T., Jones R.H. Estimation of the innovation variance of a stationary time series. Journal of the American Statistical Association 1968, 63:141-149.
18. De Bruin P., Franses P.H. Forecasting power-transformed time series data. Journal of Applied Statistics 1999, 26:807-815.
19. Diebold F.X., Mariano R.S. Comparing predictive accuracy. Journal of Business and Economic Statistics 1995, 13:253-263.
20. Engle R.F. Band spectrum regression. International Economic Review 1974, 15:1-11.
21. Fay G., Moulines E., Soulier P. Nonlinear functionals of the periodogram. Journal of Time Series Analysis 2002, 23:523-553.
22. Fernandes M., Grammig J. A family of autoregressive conditional duration models. Journal of Econometrics 2006, 130:1-23.
23. Franses P.H., McAleer M. Testing for unit roots and non-linear transformations. Journal of Time Series Analysis 1998, 19:147-164.
24. Freeman J., Modarres R. Inverse Box Cox: the power normal distribution. Statistics and Probability Letters 2006, 76:764-772.
25. Goncalves S., Meddahi N. Box-Cox transforms for realized volatility. Journal of Econometrics 2011, 160:129-144.
26. Gradshteyn I.S., Ryzhik I.M. Table of integrals, series, and products 1994, Academic Press. 5th ed.
27. Graham R.L., Knuth D.E., Patashnik O. Concrete mathematics 1994, Addison-Wesley Publishing Company.
28. Granger C.W.J., Newbold P. Forecasting transformed time series. Journal of the Royal Statistical Society, Series B 1976, 38:189-203.
29. Guerrero V.M. Time-series analysis supported by power transformations. Journal of Forecasting 1993, 12:37-48.
30. Hannan E.J., Nicholls D.F. The estimation of prediction error variance. Journal of the American Statistical Association 1977, 72:834-840.
31. Harvey D., Leybourne S., Newbold P. Testing the equality of prediction mean squared errors. International Journal of Forecasting 1997, 13:281-291.
32. Higgins M.L., Bera A. A class of nonlinear ARCH models. International Economic Review 1992, 33:137-158.
33. Hopwood W.S., McKeown J.C., Newbold P. Power transformations in time-series models of quarterly earnings per share. Accounting Review 1981, 56:927-933.
34. Lütkepohl H., Xu F. Forecasting annual inflation with seasonal monthly data: using levels versus logs of the underlying price index. Journal of Time Series Econometrics 2011, 3(1). Article 7.
35. Lütkepohl H., Xu F. The role of the log transformation in forecasting economic variables. Empirical Economics 2012, 42:619-638.
36. Mood A.M., Graybill F.A., Boes D.C. Introduction to the theory of statistics 1974, McGraw-Hill, US.
37. Nelson H.L., Granger C.W.J. Experience with using the Box-Cox transformation when forecasting economic time series. Journal of Econometrics 1979, 10:57-69.
38. Osborn D.R., Heravi S., Birchenhall C.R. Seasonal unit roots and forecasts of two-digit European industrial production. International Journal of Forecasting 1999, 15:27-47.
39. Pankratz A., Dudley U. Forecasts of power-transformed series. Journal of Forecasting 1987, 6:239-248.
40. Pascual L., Romo J., Ruiz E. Bootstrap prediction intervals for power-transformed time series. International Journal of Forecasting 2005, 21:219-235.
41. Proietti T., Riani M. Transformations and seasonal adjustment. Journal of Time Series Analysis 2009, 30:47-69.
42. Sadorsky P., McKenzie M.D. Power transformation models and volatility forecasting. Journal of Forecasting 2008, 27:587-606.
43. Tukey J.W. On the comparative anatomy of transformations. Annals of Mathematical Statistics 1957, 28:602-632.
44. Tunnicliffe Wilson G. Discussion of the paper by Dr. Chatfield and Dr. Prothero. Journal of the Royal Statistical Society, Series A 1973, 136:315-319.
45. Whittle P. Gaussian estimation in stationary time series. Bulletin of the International Statistical Institute 1962, 39:105-129.
46. Zhao-Guo C., Hannan E.J. The distribution of periodogram ordinates. Journal of Time Series Analysis 1980, 1:73-82.