# About the Multiple Cycles Indicator

Fourier analysis is coupled with Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) regression, mixed distribution estimation, and harmonic regression to detect the multiple cycle structures for 25 OECD member countries. Out-of-sample estimates indicate the current direction of economic growth. A report is published when a new quarter of GDP growth data is available from the Organisation for Economic Co-operation and Development (OECD).

### The dataset

The panel dataset contains the percentage GDP growth for 25 OECD member countries, and for Europe, as administered by the OECD. GDP growth is defined as the percentage change relative to the same period the previous year. For each of the 25 member countries, data of GDP growth is available since at least 1962 Q1.

### Model Explanation

Fourier analysis is a well-known method in mathematics, physics, and econometrics to describe the cyclic properties of a signal. A drawback of Fourier analysis is that the results are unreliable when trend and irregular components vary over time, that is, when the time series of interest displays signs of non stationarity. Therefore, we couple Fourier analysis with a GARCH model. The GARCH model enables us to flexibly model potential dynamics, trend growth, and time varying volatility. The weakly stationary standardized residuals of the GARCH model are used as the input signal in Fourier analysis. Interestingly, we find that for many member countries, both a harmonic cycle of 5 years, and a harmonic cycle of 9 years correlate strongly with the data. Given the obtained cycles and their estimated lengths, we estimate a classical trend-cycle model, where the cycles are captured using harmonic terms. The out-of-sample estimates of the harmonic regression model give an indication of the future state of the economy.

### References

de Groot, E.A., Prins, D., Segers, R., 2020. Measuring Economic Cycles in 25 OECD countries: A New Appearance of the Golden Ratio, manuscript in preparation