E Kasupovich (Bauman Moscow State Technical University) :
Articles:
Oblakova T. V. (Bauman Moscow State Technical University), Kasupovich E. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-4-111127
The paper is devoted to methods to the comparative study of parametric and nonparametric methods for detecting anomaly in time series of various nature. To solve the problem of anomaly detection in series with unknown statistical characteristics, a model based on the estimation of Kulbak-Leibler divergence between distribution laws is considered and implemented. The Kullback-Leibler importance estimation procedure (KLIEP) is applied to calculate the parameters of the linear model. A two-stage algorithm for solving the obtained conditional optimization problem by the gradient descent method was implemented using the original software code, and the cross-validation method was used to evaluate the model's learning ability. A comparative analysis of the quality of fault moment detection by the considered KLIEP method and the classical cumulative sum model (CUSUM) was carried out. When working with simulated data, insignificant variations in such characteristics of KLIEP and CUSUM models as the average time of fault detection and false alarm rate were found. For the real power mode fault detection task, both procedures showed 1-2 false alarms, but KLIEP obtained a narrower time window (5 time intervals vs. 20), which in principle allows much faster and without loss of accuracy anomaly detection. Similar results were obtained when detecting discrepancies in key performance indicators of Internet service. In general, it is shown that the KLIEP model does not degrade the quality of anomaly detection compared to popular models that use statistical characteristics of the series. The advantage of using this approach is demonstrated on real data, since it does not require knowledge of the law of distribution of the time series.
Облакова Т.В., Касупович Э. Имплементация процедуры Кульбака-Лейблера к задаче о разладке во временных рядах различной природы. Математическое моделирование и численные методы, 2024, № 4, с. 111–127.
519.2 Numerical research of persistent time series based on the ARFIMA model
Oblakova T. V. (Bauman Moscow State Technical University), Kasupovich E. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-4-114125
The work is devoted to methods for detecting long-term memory in financial time series. Using the method of analysis with the help of the original program code, a number of values of the real financial index S & P500 were studied, estimates of the Hurst index were obtained, and persistence was demonstrated. To solve the problem of predicting the future values of a series, the ARFIMA model is proposed, which is a generalization of the standard ARIMA model and involves the use of a fractional differentiation opera-tor. A two-stage algorithm for constructing a forecast for a series of logarithmic profits is presented and implemented. It is shown that the use of the ARFIMA model improves the quality of the forecast in comparison with ARIMA for all standard metrics.
Облакова Т.В., Касупович Э. Численное исследование персистентных временных рядов на основе модели ARFIMA. Математическое моделирование и численные методы, 2022, № 4, с. 114–125.