The Evolution of Economic Cycle’s Structure

In this paper, we investigate questions related to the study of the nature of oscillations and the modeling of the economic cycle on the basis of two approaches: wavelet analysis and the Bayesian approach to estimating the parameters of vector autoregression. For the wavelet analysis, we used 3 annual indicators: the Dow Jones index, the United States' GDP and the Wolf sunspots number (estimation of the solar activity) for the period from 1900 to 2015. The time-frequency analysis based on wavelets revealed stable 16-year periods of oscillations for the GDP series and the Dow Jones index, the well-known 11-year cycle for the Wolf numbers. After performing the cross-wavelet transformation, there was no revealed a stable coherence between the Dow-Jones and the Wolf numbers. To simulate economic fluctuations also in this paper were constructed two vector autoregressive models: Bayesian vector autoregression (BVAR) and Bayesian vector autoregression with Markov switching (MSBVAR). Quarterly variables of the US GDP and employment from 1953 to 2015 were used. The model parameters were estimated on the basis of a priori independent normal - Wishart inverse distribution. A graph of the regime probabilities was constructed. The adequacy of the BVAR and MSBVAR models was assessed on the basis of impulse response functions. Based on the minimization of the mean-square error of the forecast, the conclusion is being drawn about the most acceptable model and this model in our study is BVAR.