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In the context of the rapid growth of data volumes and the increasing complexity of economic, technical, and social systems, time series analysis has become a key tool for monitoring and forecasting their state. One of the most pressing tasks in working with time series is outlier detection—anomalous observations that can indicate either measurement errors or critical changes in system behavior. Traditional outlier detection methods based on univariate distribution analysis or regression residuals are often ineffective in multivariate systems where components are linked by complex nonlinear dependencies. This scientific article focuses on the application of copula models for analyzing the dependence structure in multivariate time series to enhance the efficiency of outlier detection. The theoretical foundations of copula theory, which allows for the separation of marginal distributions and the structure of interrelationships between series, are investigated. Special attention is paid to parametric and nonparametric methods for estimating copulas, as well as to the construction of statistical tests and measures based on them for identifying anomalous observations. The work demonstrates that the use of conditional copula functions makes it possible to detect objects that violate the typical dependency structure, even if they are not extreme in each individual variable. The conclusion is drawn about the high potential of the copula approach as a flexible and powerful tool for data mining, capable of accounting for a wide range of dependencies, including heavy tails and asymmetry, which is critical for reliable anomaly detection in modern complex systems.
time series, copula models, dependence structure, outlier detection, multivariate analysis, anomalies
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