Search

Detecting anomalies in temporal data is challenging due to anomalies being dependent on temporal dynamics. One-class classification methods are commonly used for anomaly detection tasks, but they have limitations when applied to temporal data. In particular, mapping all normal instances into a single hypersphere to capture their global characteristics can lead to poor performance in detecting context-based anomalies where the abnormality is defined with respect to local information. To address this limitation, we propose a novel approach inspired by the loss function of DeepSVDD. Instead of mapping all normal instances into a single hypersphere center, each normal instance is pulled toward a recent context window. However, this approach is prone to a representation collapse issue where the neural network that encodes a given instance and its context is optimized towards a constant encoder solution. To overcome this problem, we combine our approach with a deterministic contrastive loss from Neutral AD, a promising self-supervised learning anomaly detection approach. We provide a theoretical analysis to demonstrate that the incorporation of the deterministic contrastive loss can effectively prevent the occurrence of a constant encoder solution. Experimental results show superior performance of our model over various baselines and model variants on real-world industrial datasets.

Anomalies in univariate time series often refer to abnormal values and deviations from the temporal patterns from majority of historical observations. In multivariate time series, anomalies also refer to abnormal changes in the inter-series relationship, such as correlation, over time. Existing studies have been able to model such inter-series relationships through graph neural networks. However, most works settle on learning a static graph globally or within a context window to assist a time series forecasting task or a reconstruction task, whose objective is not tailored to explicitly detect the abnormal relationship. Some other works detect anomalies based on reconstructing or forecasting a list of inter-series graphs, which inadvertently weakens their power to capture temporal patterns within the data due to the discrete nature of graphs. In this study, we propose DyGraphAD, a multivariate time series anomaly detection framework based upon a list of dynamic inter-series graphs. The core idea is to detect anomalies based on the deviation of inter-series relationships and intra-series temporal patterns from normal to anomalous states, by leveraging the evolving nature of the graphs in order to assist a graph forecasting task and a time series forecasting task simultaneously. Our numerical experiments on real-world datasets demonstrate that DyGraphAD has superior performance than baseline anomaly detection approaches.

Traditionally stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths denoted as $A$, which corresponds to the notion of stationarity. On one hand, the set $A$ is shown to be large enough, so that for any stationary process, almost all of its paths are in $A$. On the other hand, we prove that any path in $A$ will behave in the optimal way under any stationarity test satisfying some mild conditions. The results provide a unified framework to understand and assess the existing time series tests for stationarity, and can potentially lead to new families of stationarity tests., Comment: 21 pages

This paper examines the effect of the proportionof females in the establishment on the male/female wage gap and the effectiveness of an affirmaive action program in reducing this gap. A unique data set makes this paper possible since it has information on both individuals and the establishments they work for. The paper documents a significant difference in the sex composition of the establishments in which males and females work. Further, it is shown that the proportion of females in the establishment is negatively related to the wages of both males and females and accounts for 26 percent of the gap in log wages between men and women. Due to an inadequacy of the traditional method of decomposing wages when examining an affirmative action program, a new method of decomposition is developed: the characteristic wage decomposition. The results suggest that an employment equity program will reduce the male/female log wage gap by 20 percent.

We examine the ability of the simple linear-quadratic model under rational expectations to explain dynamic behaviour of aggregate Canadian imports. In contrast to authors of previous studies who examine dynamic behaviour using the LQ model, we estimate the structural parameters using the Euler equation in a limited information framework that does not require an explicit solution for the model's control variables in terms of the exogenous forcing variables., Dans le pr��sent article, les auteurs cherchent �� ��tablir si le mod��le simple de forme quadratique lin��aire peut, sous l'hypoth��se de rationalit�� des attentes, expliquer le comportement dynamique de l'ensemble des importations canadiennes. Contrairement aux auteurs d'��tudes ant��rieures, ax��es sur la m��thode quadratique lin��aire, ils estiment les param��tres structurels �� l'aide de l'��quation d'Euler en utilisant une m��thode du maximum de vraisemblance �� information limit��e qui n'exige pas que les variables de contr��le du mod��le soient explicitement r��solues en fonction des variables d'impulsion exog��nes.

In a recent paper Mercenier and Sekkat (1988) conclude that the Bank of Canada has followed a policy of exchange rate targeting using the money supply. We re-examine their results using a different estimation approach and with different assumptions about the forcing process of the exogenous variables., Dans une ��tude publi��e en 1988, Mercenier et Sekkat ont conclu que la Banque du Canada avait des objectifs en mati��re de taux de change qu'elle cherchait �� atteindre en influant sur la masse mon��taire.

We examine whether there is a significant relationship between government and private consumption for Canada. We derive estimating equations between the two types of consumption under both cointegration and no-cointegration assumptions.