A major concern when dealing with financial time series involving a wide variety of market risk factors is the presence of anomalies. These induce a miscalibration of the models used to quantify and manage risk, resulting in potential erroneous risk measures. We propose an approach that aims to improve anomaly detection in financial time series, overcoming most of the inherent difficulties. Valuable features are extracted from the time series by compressing and reconstructing the data through principal component analysis. We then define an anomaly score using a feedforward neural network. A time series is considered to be contaminated when its anomaly score exceeds a given cutoff value. This cutoff value is not a hand-set parameter but rather is calibrated as a neural network parameter throughout the minimization of a customized loss function. The efficiency of the proposed approach compared to several well-known anomaly detection algorithms is numerically demonstrated on both synthetic and real data sets, with high and stable performance being achieved with the PCA NN approach. We show that value-at-risk estimation errors are reduced when the proposed anomaly detection model is used with a basic imputation approach to correct the anomaly.

This papers derives finite sample results to assess the consistency of Generalized Pareto regression trees introduced by Farkas et al. [2021] as tools to perform extreme value regression for heavy-tailed distributions. This procedure allows one to constitute clusters of similar tail behaviors depending on the value of the covariates, based on a recursive partition of the sample and simple model selection rules. The results we provide are obtained from concentration inequalities, and are valid for a finite sample size. A misspecification bias that arises from the use of a Peaks over Threshold approach is also taken into account. Moreover, the derived properties legitimate the pruning strategies, that is the model selection rules, used to select a proper tree that achieves a compromise between simplicity and good fit. The methodology is illustrated through a simulation study, and a real data application in insurance against natural disasters.