## 3 Results  
The comparative study with traditional multiclass classifiers is detailed, combining objective quantitative outcomes with contextual qualitative assessments informed by domain-specific knowledge. The results are based on detailed tests using the Galati County dataset, after applying all the data preparation and target definition steps mentioned earlier. The analysis is presented in a clear and structured way, starting with basic statistics and visual graphs, and then moving on to model evaluation and interpretation of the main findings. An initial investigation showed some significant patterns in terms of spatio-temporal dependencies and the relationships between socioeconomic predictors and the standardized crime rate. Figure 2 shows the time series plot of the normalized monthly relevant explanatory variables, i.e., the unemployment rate, the net salary adjusted by inflation, the number of tourist arrivals and the international trade balance. The figure shows obvious evidence of synchronized peak holdings--especially in downturns and when being shocked--such that unemployment rate, crime rate and net salary co-move upwards and tourist arrivals plunge. These results are consistent with the existing literature on the marriage between economic hardship and the surge in crime [47; 48]. Seasonal effect is also found with high temperature and high crime activity similar to touristic districts during summer time and so the seasonal lags and dummy variables are put in the model [49]. Setting up the new multiclass target \"Crime risk\" allowed us to implement a balanced classification problem as exhibited by the profile of the temporal distribution of risk classes  
Figure 2: Dynamics of standardized explanatory variables. in Figure 3. Visually, it appears that regime transitions are triggered by macroeconomic or policy events, as abrupt transitions in class membership from moderate or low risk to high or very high risk are observed in the case of lockdown due to COVID-19. The balanced five-class stratification prevents class imbalance bias in the model learning process, as can be noted from the well-balanced distribution of the cases and the well-visible regime transitions in the visualization [50]. The time series decomposition and the autocorrelation analyses shown in Figure 4 identified the short-term autocorrelation (lag 1-3 months), as well as a prominent annual seasonality (lag 12 months), which supported the application of an ARIMA model with non-seasonal and seasonal components. Looking at the PACF, we see most of the linear signal can be handled by a simple autoregressive model of order 1 or 2 (denoted \(AR(1)\) or \(AR(2)\)), meaning that the current crime rate can be effectively predicted using one or two preceding values, with higher lags providing little additional explanatory power. These results demonstrated that the ARIMA model can capture the linear and periodic structure of the crime rate sequence, making it easier for the next ANN step to work with a clearer, more refined set of residual values [51]. The performance of the hybrid ARIMA-ANN model was compared to classical multi-class classifiers: multinomial logistic regression, decision trees, random forests, support vector machines. All models were trained and validated with five-fold stratified cross-validation to ensure that class balance and temporal structure were maintained. We use the key performance metrics--accuracy, macro-averaged precision, recall, F1-score, and AUC-ROC--for each classifier, as presented in Table 2. The hybrid ARIMA-ANN model generalizes well out of sample and tends to outperform all benchmarks, presenting an overall accuracy of 76.4%, a macro F1-score of 0.762, and an AUC-ROC of 0.882 against  
Figure 4: ACF and PACF of crime rate. Figure 3: Distribution of crime risk classes over time. The confusion matrix of the hybrid model is highly diagonally concentrated, with most errors made between neighboring classes (indicated by models) \"moderate\" and \"high\" risk rather than between extreme classes.