After the trend values and seasonal variations are eliminated from a time series, there will remain the components of only cyclical and irregular variations i.e. C & I. The analysis of time series will not be complete unless the cyclical fluctuations are measured, and separated from the irregular or random variation. Moreover, the business cycles are the most important type of fluctuations in economic data, and they extend over a comparatively long period of time than the seasonal variations. But this is a very difficult task to measure the cyclical variations, and there is no well recognized method for the purpose. This is because, the cyclical rhythm is inextricably mixed up with the irregular factors, and they vary widely in timing, amplitude and pattern as well. As such, it is quite impossible to compute the meaningful typical indices, or to fit curves for the cyclical variations as they are possible in case of the trend and seasonal measurements.
However, Professors Croxton & Cowden have propounded the following four methods in their work entitled “Applied General Statistics” for measuring the cyclical variations in a time series.
- Residual method.
- Direct percentage method
- Harmonic analysis method
- Reference cycle analysis method