This chapter outlines a statistical methodology for phasing historical trend periods. The first section is a review of the statistical methodology that has been employed to analyse long-term growth phases in previous literature. The next section outlines the statistical methodology followed in this study.

The existing statistical methodology

The statistical methodology of the early work on trend periods was mechanistic in nature, neglecting the economic implications of the statistical transformations. Kondratief's (1979) methodology was to fit ordinary least squares (OLS) trend lines to time series data and take a nine-year moving average of the residuals to eliminate the Juglar cycle. The idea that the trend line was constant over the period of his study (1780–1920) assumes that the economic structure remained unchanged. The nine-year moving average assumes that trends and cycles are additive and one can be removed from the other. Even if this assumption holds, the use of the nine-year moving average will serve its purpose only if the cycle is, in fact, exactly nine years. The actual cycle is variable in length and random variation. In such cases the moving-average process will only serve to produce longer cycles. A fixed moving-average process is being applied to an irregular cycle and, thus, will capture the summation of random factors. Slutsky (1937) has shown that the movingaverage process when applied to random numbers may create cyclical fluctuations where none existed before.