Objective:

Determine the existence of the Political Business Cycle (PBC) in Mexico for the 1980-2021 period through a mathematical method of physics, which has not been used in the field of political economy.

Methodology:

Economic growth and inflation in Mexico are studied through the PBC theory using a Fourier series analysis, which allows us to study the behavior of a cyclical function.

Results:

The presence of the PBC has been confirmed during the last four decades in Mexico, where a considerable difference was found in the data of the last year of government as compared to the approximation made by Fourier series.

Limitations:

Although there are other methods that incorporate the random component of a time series within the estimation, the Fourier series analysis is deterministic. However, this has become an explanatory element within the application of Fourier series in the field of economics.

Originality:

It is the first time that an approximation of the PBC through Fourier series has been carried out in Mexico, since the traditional methodology to estimate the PBC consists of autoregressive models with electoral dummy variables. Therefore, this paper might be considered as a pioneering econophysics study.

Conclusion:

It is concluded that the approximation of economic growth and inflation under the PBC theory carried out with Fourier series of one iteration, allows to identify a deterministic trend and a stochastic component, which not only confirms the existence of the PBC, but also leads to determine its intensification during the last year of government.