Використання ARIMA моделей для прогнозування загального рівня злочинності в Україні

Abstract

Crime rate forecasting is a critical element in the development of strategies for sustainable socio-economic growth in a rule-of-law state. Accurate forecasting becomes particularly important in times of economic instability and geopolitical crises, as is the case in Ukraine. This article explores the problem of constructing and applying autoregressive integrated moving average (ARIMA) models to predict the total number of crimes committed in Ukraine. The statistical analysis of the crime time series was conducted using the Python programming language, utilizing specialized libraries such as numpy, pandas, matplotlib, statsmodels, pmdarima, and scikit-learn. The calculations indicate that the crime time series (1990-2023) demonstrates a declining trend, is non-stationary, and contains anomalous values in crime rates in 2003, 2013, and 2020, correlating with socio-political crises in Ukraine. Specifically, the anomalous increases in crime rates (in 2003 and 2013) align with heightened public unrest preceding the Orange Revolution (2004-2005) and the Revolution of Dignity (2013-2014). In contrast, the unusually low crime rates observed in 2020 are attributed to restrictive quarantine measures implemented due to the COVID-19 pandemic. The use of data integration by taking the first differences between observations resulted in the loss of autocorrelation structure inherent in the overall crime series. Consequently, the initial ARIMA (1, 0, 0) model was built based on the untransformed input data. The accuracy of this model was higher compared (MAPE = 8,61%) to the model obtained using the exponential smoothing method (MAPE = 9,38%). Logarithmic transformation of the crime time series and smoothing of anomalous levels enhanced the predictive validity, allowing the ARIMA model to account for additional autocorrelation while avoiding the need for a moving average component. As a result, the ARIMA (2, 0, 0) model demonstrated the highest accuracy (MAPE = 7,04%) with minimal complexity, as confirmed by information criteria results. Furthermore, the model successfully passed robustness testing using the cross-validation method with the exclusion of a single observation. The forecasted estimates, derived from all the examined ARIMA models, indicate a continued increase in the overall crime rate in Ukraine, which began in 2021 following a prolonged period of decline.