Production of sugar beet in Russian Federation: analysis and forecast

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Introduction
The production and consumption of sugar (and, as a result, sugar beets) can be regarded as an indicator of economic and political stability in our country, since any fluctuations lead to a rush demand for this product [1][2][3][4][5].
In European countries, beet sugar produces up to 80% of the total collection in the world [6].China, the world's fourth-largest sugar producer after Brazil, India, and the European Union, 20% of sugar comes from sugar beets [7].Sugar beet requires an abundance of sun, warmth and moderate humidity, therefore, in the Russian Federation, the cultivation of this crop is concentrated in the southern regions.On the lands of the Krasnodar region, the Volga and Chernozem regions, 51% of the total sugar beet is grown [7][8][9][10].
The purpose of this work is to consider the current state and trends in the production of sugar crops in the country and, based on the analysis, give a forecast for the development of the industry.

Materials and methods
The object of study in the work was shown, characterizing the process of growing sugar beets in the Krasnodar region, the Penza region and the Russian Federation as a whole.In particular, y1 -sown area, thousand ha, y2 -gross harvest, million tons, y3 -yield, cwt/ha.The information base of the study was the data of the Federal State Statistics Service [11].The time interval of the study is the period from 2005 to 2021.Regression parameters were calculated using the STATISTICA package [12][13].The results of the research are presented in graphical forms.

Results and Discussion
Primary analysis of data based on indicators of time series dynamics makes it possible to conclude that over the considered period of time [11][12][13][14][15][16][17][18], the volume of acreage allocated for sugar beet increased in all the studied regions (Fig. 1).For example, in the Penza region, the average growth was 3.8% per year, or 1.9 thousand hectares per year; in the Krasnodar region 5.15% or 8.84 thousand hectares; as a whole in the Russian Federation 2.7% or 27.7 thousand hectares per year.The strongest growth in sown areas in all regions was in 2010 (41% in the whole of the Russian Federation).
Conducting a component analysis of time series in order to model further changes in the dynamics of sown areas, a two-sample F-test for variance was carried out [12,[19][20][21][22][23][24][25], which showed the presence of a trend in all-time series, since, for example, the value of variances at the beginning and at the end of the time series for sown areas area in the Russian Federation differs by 2.8 times.Similarly for the time series of the Krasnodar region and the Penza region.
Carrying out a comparative analysis of several regression equations, the following were chosen as the trend equation in time series describing the dynamics of changes in sugar beet sown areas [26][27]: -according to the Russian Federation: quadratic function y11=796.07+46.8t+1.89t 2 +ɛ, coefficient of determination R 2 =0.521, hypotheses about the significance of parameters are accepted; -for the Krasnodar region: exponential function y12=148.5e 0.01t , R 2 =0.514, parameters are significant; -for the Penza region: a linear function y13=38.35+1.24t+ɛ,R 2 =0.725, the parameters are significant.
Based on the analysis of the autocorrelation function, which for the RF series took the values ƒ(τ=1) =0.36, ƒ(τ=2) =0.32, ƒ(τ=3) =0.31, ƒ(τ=4)=0.02,ƒ(τ=5)=0.28,we can conclude that there is a cyclical component in the dynamics of changes in sugar beet acreage in the whole of the Russian Federation with a period of τ=5.In addition, the analysis of Fig. 1 makes it possible to assume a multiplicative relationship between the main trend and the cyclical component in the dynamics of time series [28][29][30][31][32].
Indicators of periodic fluctuations are seasonality indices, which show the differences between the corresponding levels of the series from the main trend.To determine them, it is necessary to find the average values of the same-name levels of the series composed of the ratios of the original series and the corresponding smoothed values using the trend equation [2].
The indicated values indicate that in each five-year period, in the second and third years, there is an increase in the acreage of sugar beet by 8.6% -11.1% relative to the average level set by the trend; in the remaining three years, there is a decrease of 2.5%, 7% and 6%, respectively.The coefficient of approximation of the obtained trend-seasonal model was A=7.8%.
The resulting models can be used to predict the dynamics of sown areas devoted to sugar beet in the regions of Russia [33][34][35][36][37][38][39].So, for example, in 2023 the sown area of the Penza region should be 68.3 thousand ha, in 2024 -60.9 thousand ha; in the Krasnodar region in 2013, the area will amount to 231.1 thousand ha, in 2024 -182.9 thousand ha; in general, in the Russian Federation 1112.5 thousand ha and 889.9 thousand ha, respectively.Fig. 2. Gross harvest of sugar beet, million tons [11].
Analyzing the gross harvest of sugar beet by regions of the Russian Federation (Fig. 2), it can be noted that there are general positive development trends [40][41][42][43][44][45].The highest growth in the harvest of sugar beet was shown by the Penza region: an average of 18.8% or 0.3 million tons over the period, the average growth of the Krasnodar region was 10.5% or 0.77 million tons, the average growth in the whole of the Russian Federation amounted to 8.6% or 3.2 million tons.The largest growth in all regions occurred in 2011 (114% in the whole of the Russian Federation), which was the result of an increase in sown areas in 2010.
Similarly, to the above, in the time series of the gross harvest of sugar beet there is a multiplicative effect of the periodic component (period τ=5): -for the Russian Federation:  When analyzing sugar beet yields by regions of the Russian Federation (Fig. 3), one can note a general increase in time series trends, which indicates an increase in yield, as well as a lower volatility of processes, which indicates stability in yield dynamics.The average increase in the yield of sugar beet in the whole of the Russian Federation was 4.5% or 17.2 cwt/ha, in the Krasnodar region -6.2% or 26.7 cwt/ha; in the Penza region -10.2% or 33.5 cwt/ha.
In other words, the general combination of soil composition, seeds, fertilizers and plant care in the agricultural enterprises of the Penza region makes it possible to obtain large yields of sugar beet on smaller areas [53].
The periodic component in all series has a multiplicative direction and period τ=5:

Conclusion
In conclusion, it should be noted that the production of sugar and sugar beet in the Russian Federation fully covers the needs of consumers.This sector of agricultural production has a steady upward trend.As the results of the study showed, the forecast for the gross harvest of sugar beets: in the Russian Federation: in 2023 -41.
2 million tons, in 2024 -38.12 million tons; in the Krasnodar region: in 2023 8.02 million tons, in 2024 7.7 million tons; in the Penza region: in 2023 2.56 million tons, in 2024 2.42 million tons.