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EN
The subject of this work is a comparative analysis of selected models used to describe the volatility of time series including exceptions. This paper is focus on the the dynamic properties of the time series, generallyon the heterogeneity of conditional variance over time. This paper describes common approaches to detecting outliers, modelling and forecasting time series. Based on the researches performed by R. F. Engle, T. B. Bollerslev, J. Caiadoin, were examined selected ARIMA, ARCH and GARCH.An attention was paid to the ARCH effect in time series and its impact on the modelling volatility of financial time series, which contain outliers. The studies showed that the typical features of financial time series are the so-called grouped variances. Therefore, using ARIMA models for forecasting was insufficient, ARCH and GARCH modelsshowed good statistical properties for modelling time series data.
PL
Przedmiotem niniejszej pracy jest analiza porównawcza wybranych modeli służących do opisu zmienności szeregów czasowych, w tym wyjątków. Artykuł koncentruje się na dynamicznych właściwościach szeregów czasowych, na ogół na heterogeniczności warunkowej wariancji w czasie. W niniejszym artykule opisano powszechne metody wykrywania wartości odstających, modelowania i prognozowania szeregów czasowych. Na podstawie badań przeprowadzonych przez RF Engle, TB Bollerslev, J. Caiadoin, zbadano wybrane ARIMA, ARCH i GARCH. Zwrócono uwagę na efekt ARCH w szeregach czasowych i jego wpływ na zmienność modelowania finansowych szeregów czasowych, które zawierają odstające. Badania wykazały, że typowymi cechami finansowych szeregów czasowych są tak zwane pogrupowane wariancje. Dlatego wykorzystanie modeli ARIMA do prognozowania było niewystarczające, modele ARCH i GARCH prezentowały dobre właściwości statystyczne do modelowania danych szeregów czasowych.
EN
This research contribution instantiates a framework of a hybrid cascade neural network based on the application of a specific sort of neo-fuzzy elements and a new peculiar adaptive training rule. The main trait of the offered system is its competence to continue intensifying its cascades until the required accuracy is gained. A distinctive rapid training procedure is also covered for this case that offers the possibility to operate with non-stationary data streams in an attempt to provide online training of multiple parametric variables. A new training criterion is examined for handling non-stationary objects. Additionally, there is always an occasion to set up (increase) the inference order and the number of membership relations inside the extended neo-fuzzy neuron.
EN
Several operational security mechanisms have been developed to mitigate malicious activity in the Internet. However, the most these mechanisms require a signature basis and present the inability to predict new malicious activity. Other anomaly-based mechanisms are inefficient due to the possibility of an attacker simulates legitimate traffic, which causes many false alarms. Thus, to overcome that problem, in this paper we present an anomaly-based framework that uses network programmability and machine learning algorithms over continuous data stream. Our approach overcomes the main challenges that occur when develop an anomaly-based system using machine learning techniques. We have done an experimental evaluation to demonstrate the feasibility of the proposed framework. In the experiments, we use a DDoS attack as network intrusion and we show that the technique attains an Accuracy of 98.98%, a Recall of 60%, a Precision of 60% and an FPR of 0.48% for 1% DDoS attack on the real normal traffic. This shows the effectiveness of our technique.
EN
Two types of heuristic estimators based on Parzen kernels are presented. They are able to estimate the regression function in an incremental manner. The estimators apply two techniques commonly used in concept-drifting data streams, i.e., the forgetting factor and the sliding window. The methods are applicable for models in which both the function and the noise variance change over time. Although nonparametric methods based on Parzen kernels were previously successfully applied in the literature to online regression function estimation, the problem of estimating the variance of noise was generally neglected. It is sometimes of profound interest to know the variance of the signal considered, e.g., in economics, but it can also be used for determining confidence intervals in the estimation of the regression function, as well as while evaluating the goodness of fit and in controlling the amount of smoothing. The present paper addresses this issue. Specifically, variance estimators are proposed which are able to deal with concept drifting data by applying a sliding window and a forgetting factor, respectively. A number of conducted numerical experiments proved that the proposed methods perform satisfactorily well in estimating both the regression function and the variance of the noise.
EN
The research described in this paper concerns the reduction of streams of data derived from medical devices, i.e. ECG recordings. Experimental studies included three instance selection techniques: thresholding method, bounds checking and frequent data reduction . It was shown that application the instance selection techniques may reduce data stream by over 90% without losing anomalies or the measurements that are key values for the medical diagnosis.
PL
W ramach niniejszej pracy przeprowadzona została redukcja strumienia danych pozyskanych z urządzeń medycznych. Badania eksperymentalne obejmowały zastosowanie trzech technik selekcji przypadków: metody eliminacji progowej, weryfikacji zakresu oraz redukcji obiektów częstych. W pracy zostało wykazane, że zastosowanie selekcji przypadków pozwala na redukcję strumienia danych o ponad 90% bez utraty wartości kluczowych dla postawienia diagnozy medycznej.
EN
Data streams (streaming data) consist of transiently observed, evolving in time, multidimensional data sequences that challenge our computational and/or inferential capabilities. We propose user friendly approaches for robust monitoring of selected properties of unconditional and conditional distributions of the stream based on depth functions. Our proposals are robust to a small fraction of outliers and/or inliers, but at the same time are sensitive to a regime change in the stream. Their implementations are available in our free R package DepthProc.
EN
In this paper, we introduce a method for survival analysis on data streams. Survival analysis (also known as event history analysis) is an established statistical method for the study of temporal “events” or, more specifically, questions regarding the temporal distribution of the occurrence of events and their dependence on covariates of the data sources. To make this method applicable in the setting of data streams, we propose an adaptive variant of a model that is closely related to the well-known Cox proportional hazard model. Adopting a sliding window approach, our method continuously updates its parameters based on the event data in the current time window. As a proof of concept, we present two case studies in which our method is used for different types of spatio-temporal data analysis, namely, the analysis of earthquake data and Twitter data. In an attempt to explain the frequency of events by the spatial location of the data source, both studies use the location as covariates of the sources.
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