Selecting a linearizing power transformation for time series

A method is proposed for choosing a power transformation that allows a univariate time series to be adequately represented by a straight line, in an exploratory analysis of the data. The method is quite simple and enables the analyst to measure local and global curvature in the data. A description of the pattern followed by the data is obtained as a by-product of the method. A specific form of the coefficient of determination is suggested to discriminate among several combinations of estimates of the index of the transformation and the slope of the straight line. Some results related to the degree of diff erencing required to make the time series stationary are also exploited. The usefulness of the proposal is illustrated with four empirical applications-two using demographic data and the other two concerning market studies. These examples are provided in line with the spirit of an exploratory analysis, rather than as a complete or confirmatory analysis of the data.