Cycle Skew Factors: Asymmetric Business Cycles

Please check out our updated article on “Asymmetric Business Cycles and Skew Factors” in the latest CYCLES MAGAZINE, the official journal of the Foundation for The Study of Cycles:

Cycle analysis and cycle forecasting often imply the use of a symmetric time distribution between high to low and low to high. This is the underlying framework used by anyone applying mathematical signal processing to cycles and producing cycle-based composite cycle forecasts. This technique is now faced with a new challenge that has emerged over the past 30 years based on financial regulations impacting today’s economic business cycle. The following article will highlight the situation and present the reader with a proposed skew factor to account for this behavior in cycle forecasting models.  […]

Since 2-phase cycle models are based on a time-symmetric distribution of dominant cycles with mathematical sine-based counting modes from low to low or high to high. However, these models lose their forecasting ability under the assumption that a uniform distribution from high to low and low to high is no longer given.

A new model is needed. A dynamic skew cycle model that includes a skew factor.

A common approach is to build cycle prediction models based on detected or predefined values for cycle length, phase, and amplitude. These models use a standard sine wave function to create a cycle forecast or composite forecast projection. To retain these models and not recreate an existing model, the proposal presented in this paper is to simply replace the existing standard sine wave function with the new skewed sine wave function. Thus, any cycle prediction algorithm can remain as is and use the detected cycles with length, amplitude, and phase as input parameters. At the same time, the projection function is replaced with the new skewed sine function instead of the standard sine function.

The main features of this function in brief:

  • It is designed as a drop-in replacement for existing sine or cosine functions used for cycle prediction. It is not necessary to adjust the existing overall model. Simply use this function as a drop-in replacement in an existing algorithm.
  • A skew factor of 0.3-0.4 should be used to fit the model according to current scientific evidence on the asymmetry of the business cycle.
  • The cycle will not be skewed. The length is preserved. Thus, the top-to-bottom and bottom-to-top cycle counts are preserved and are not distorted. The amplitude will not be distorted either. In this way, it is a safe replacement, with the main cycle parameters of length and amplitude remaining intact.