We propose a novel framework that harnesses the power of generative artificial intelligence and copula-based modeling to address two critical challenges in multivariate time-series analysis: delivering accurate predictions and enabling robust anomaly detection. Our method, Copula-based Conformal Anomaly Identification for Multivariate Time-Series (CoCAI), leverages a diffusion-based model to capture complex dependencies within the data, enabling high quality forecasting. The model's outputs are further calibrated using a conformal prediction technique, yielding predictive regions which are statistically valid, i.e., cover the true target values with a desired confidence level. Starting from these calibrated forecasts, robust outlier detection is performed by combining dimensionality reduction techniques with copula-based modeling, providing a statistically grounded anomaly score. CoCAI benefits from an offline calibration phase that allows for minimal overhead during deployment and delivers actionable results rooted in established theoretical foundations. Empirical tests conducted on real operational data derived from water distribution and sewerage systems confirm CoCAI's effectiveness in accurately forecasting target sequences of data and in identifying anomalous segments within them.

In this paper we apply Conformal Prediction (CP) to the k-Nearest Neighbours Regression (k-NNR) algorithm and propose ways of extending the typical nonconformity measure used for regression so far. Unlike traditional regression methods which produce point predictions, Conformal Predictors output predictive regions that satisfy a given confidence level. The regions produced by any Conformal Predictor are automatically valid, however their tightness and therefore usefulness depends on the nonconformity measure used by each CP. In effect a nonconformity measure evaluates how strange a given example is compared to a set of other examples based on some traditional machine learning algorithm. We define six novel nonconformity measures based on the k-Nearest Neighbours Regression algorithm and develop the corresponding CPs following both the original (transductive) and the inductive CP approaches. A comparison of the predictive regions produced by our measures with those of the typical regression measure suggests that a major improvement in terms of predictive region tightness is achieved by the new measures.