Modeling Tax Revenues Using Kernel Approach Case Study: North Kivu Province (Democratic Republic of Congo) Tax Revenues Time Series Forecasting

Forecasting the distribution of tax revenues in the Democratic Republic of Congo has been an uphill task. The recent past of the country has been dominated by economic uncertainty, particularly in mining and in agricultural products (cash crops) meant for export. This factor alone has greatly contributed to high volatility of tax revenues collected by the custom officers. The fuzzy characteristic of Tax Revenues has made it quite impossible for researcher to detect or distinguish from randomness the three well known components of a classical time series, precisely Trends, Seasonality, and cyclical phenomena. Hence parametric methods, however rich appear not to be suitable at all to produce reliable forecasts. The current project focuses on modeling tax revenues time series using nonparametric method, mainly the kernel approach. Several kernels have been discussed in literature. In this project, due to its optimal property, the Epanechnikov kernel is used as an index kernel to model the time series under investigation. Other commonly kernels, including the Parzen, Gaussian, Biweight, cosine, rectangle, triangle and the alternative Epanechnikov (epan2) kernels have been used to fit the dataset and their performance compared with the index kernel. By default, the Gaussian and the alternative Epanechnikov kernels performed very close to the index kernel. Having chosen to use, for comparison purposes, the Epanechnikov, the Gaussian and the alternative Epanechnikov kernels, an optimal choice of the bandwidth has been discussed through the kernel weighted polynomial smoothing setup. Two crucial aspects of the problem were evaluated, including the degree of the polynomial that precisely fit the data points and the level of the bandwidth that is required to achieve bell-fit. To this end, the performance of the Epanechnikov, the Gaussian and the alternative Epanechnikov (epan2) kernel using kernel weighted polynomial of degrees 1, 3 and 7 for different values of the bandwidth, precisely for h = {1, 5, 7, 10} has been examined. As expected, findings suggest unequivocally that the higher the degree of the kernel weighted local polynomial smoothing combined with the smallest value of the bandwidth, the better is the fit of the kernel used to the tax revenues data. Hence, to predict or forecast tax revenues, either the Epanechnikov, the Gaussian or the alternative Epanechnikov (epan2) kernel can be used, with a careful choice of the pair (p, h) where p is the degree of the polynomial which is assumed to be reasonably high and h is the optimal bandwidth.