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Forecasts of power‐transformed series
Author(s) -
Pankratz Alan,
Dudley Underwood
Publication year - 1987
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.3980060403
Subject(s) - series (stratigraphy) , metric (unit) , mean squared error , mathematics , conditional expectation , range (aeronautics) , statistics , forecast error , gaussian , inverse , econometrics , economics , paleontology , operations management , materials science , physics , geometry , quantum mechanics , composite material , biology
Consider a time series transformed by an instantaneous power function of the Box‐Cox type. For a wide range of fractional powers, this paper gives the relative bias in original metric forecasts due to use of the simple inverse retransformation when minimum mean squared error (conditional mean) forecasts are optimal. This bias varies widely according to the characteristics of the data. A fast algorithm is given to find this bias, or to find minimum mean squared error forecasts in the original metric. The results depend on the assumption that the forecast errors in the transformed metric are Gaussian. An example using real data is given.