## 3 Results
This is a desirable property to consider when crafting risk stratification models, as errors made in low adjacent classes have diminished operational implications when compared to classifying periods of very high risk as very low risk, or vice versa [41]. The performance of the hybrid model is also shown by the ROC analysis showing strong discriminative ability of the model among classes and especially high sensitivity and specificity for \"high\" and \"very high\" risk periods. Figure 7 shows the predicted versus actual risk class trajectories for the test period (2022-2024), indicating temporal consistency of predictions of the ARIMA-ANN model with ground truth labels. The hybrid model parallels the initiation and cessation of high-risk time-frames, predicting crime spikes during post-pandemic recuperation and times of financial strain. Comparative examination with other classifiers demonstrates that the ARIMA-ANN model tends to make earlier predictions with fewer missed hits within high-risk windows, a characteristic that has straightforward operational implications for proactive policing and resource deployment [4]. The variable importance analysis (Figure 8) shows that unemployment rate, inflation-adjusted net salary and international trade balance are the most important drivers of risk classification in both the tree-based model and as feature weights of the ANN part. Figure 8: Variable importance (ARIMA-ANN). Figure 7: Predicted vs. actual risk classes (2022–2024). The findings are aligned with theory and evidence, which suggest that exposure to socioeconomic hardship and market volatility is predictive of crime risk profile [53]. Furthermore, the addition of tourist arrivals and weather factors increased the precision of the model in summer and holiday periods, when the vulnerability of tourist areas to crime increases seasonally. To enhance transparency regarding the ARIMA-ANN collaboration, the structure and nature of the nonlinear residuals produced by the ARIMA model were analyzed. After ARIMA fitting, the residuals--i.e., the portion of the time series not explained by linear autoregressive and seasonal effects were statistically examined for nonlinearity using methods such as the BDS (Brock-Dechert-Scheinkman) test and visualized via residual-vs-fitted plots. These analyses, presented in Figures 9 and 10, consistently revealed that the ARIMA residuals displayed complex patterns, particularly around sudden macroeconomic shocks (e.g., the COVID-19 lockdown period), as well as during periods of marked changes in unemployment, net salary, or population migration. For example, in 2020-2021, the ARIMA residuals showed clear bursts of volatility and sign changes, confirming the presence of underlying nonlinear dynamics. This validated the need for a nonlinear learner (ANN) in the second stage. Furthermore, autocorrelation of the residuals at nontrivial lags supported the inclusion of multiple residual lags as ANN inputs, allowing the neural network to capture both short memory effects and nonlinear dependencies missed by ARIMA alone. Figure 10: ARIMA residuals over time (2020–2021 volatility). Figure 9: Residuals vs. fitted values for ARIMA model (2020–2021 nonlinear bursts). To address the inherent 'black box' nature of the hybrid ARIMA-ANN model, particularly concerning its application in contexts requiring transparent decision-making, such as police resource allocation, advanced model interpretability techniques were incorporated. Sensitivity analysis was performed by systematically varying key socioeconomic and environmental input variables, such as 'International trade balance Exports--Imports,' 'actual employees number, 'average net salary updated with inflation', and 'unemployed people number.' The impact of these perturbations on the predicted 'Crime risk' levels was observed, providing understanding of the direct influence of individual factors on forecast outcomes. Furthermore, Explainable AI (XAI) methodologies, specifically SHAP (SHapley Additive exPlanations), were employed.