Abstract: this article discusses the theoretical aspects of the construction of ARCH and GARCH models, paid attention to the consideration of indicators such as kurtosis and excess coefficient. When comparing ARCH and GARCH models, the information criteria of Akaike, Schwartz, Hannan-Quinn are used and the best model will be the one that has the minimum values of these indicators. To analyze the volume of crude oil production in the Stavropol region, a time series graph and ACF and PACF correlograms are first constructed, in which the process of random walk is detected. The ACF gradually decreases, tending to zero from the 12th time period, and the PACF is finite, with a break after the 1st period. The parameters of crude oil production cost change for ARCH (1) and GARCH (1,1) models are estimated. The correlogram of the squares of the residuals of these models showed that the residuals are not correlated. The results of the kurtosis calculated by the GRETL program for the GARCH (1,1) model and the theoretical kurtosis calculated by the formula are compared. It was concluded that the ARCH(1) model is the most suitable for estimating this time series, as the values of the AIC, SIK, HQIC criteria for this model are less than those of the GARCH(1,1) model.
Keywords: time series, ARCH- and GARCH- models, expectation, variance, kurtosis, correlogram