Recovering the actual trajectory of economic cycles

The paper deals with the development of a method for restoring the trajectory of economic cycles from estimates of the gross domestic product (GDP). The proposed approach to solve this problem is based on the interpretation of cycles in the form of random oscillations of the income with a certain natural frequency, also called a narrowband random process. The operators (Fourier transforms, filtering, etc.) used to recover the cycle trajectory are linear. Their inherent associativity property allows changing the sequence of implementation of the linear operators above. As a result, it is proposed to start the recovery with bandpass filtering of the GDP function, and after that to parry the influence of the inertia property of the GDP estimator. Taking the qualities of a narrowband random process into consideration made it possible to create a simplified procedure to recover the cycle trajectory. In the example of the Kuznets swing, the acceptability of this procedure is demonstrated for the practical econometrics. The developed method is applicable in problems that require knowledge of the trajectory of the considered cycle.