Wavelet analysis of time series in the model of nomads and tillers

The article is devoted to the study of time series obtained in earlier works by econometric and wavelet analysis. At the first stage of this study, econometric analysis was conducted, regression was constructed. In the regression influence of the number of nomads and the amount of resource on the number of plowmen was studied. The coefficient of determination (R2) of the constructed regression turned out to be 0.81, the Durbin-Watson statistics equals to 0.94, which indicates the presence of positive first-order autocorrelation of errors. The next stage is an analysis based on wavelet transforms, which helps to get rid of high-frequency "noise" and interference in considered time series. Within the framework of this paper, the Haar wavelet and the Daubechies 2 tap wavelet were considered (the remaining wavelets give similar results). After the time series had been cleared by the wavelet analysis, regression analysis was applied again. The coefficient of determination of new regressions depending on which wavelet was applied and the interference of what frequency were removed took values in the range from 0.86 to 0.93. The coefficient of determination of new regressions depends on which wavelet was applied and the interference of what frequency were removed. It takes values in the range from 0.86 to 0.93. However, the Durbin-Watson statistics decreased its values and began to take values in the range from 0.01 to 0.46, which still indicates the presence of positive first-order autocorrelation of errors. In the end, we learn that in this situation, the application of wavelet analysis significantly increases the explanatory power of regression, on the other hand, the problem of autocorrelation of errors can not be resolved in this way, in some sense it is only getting worse.