The article describes an approach to modelling and forecasting non-linear non-stationary time series for various purposes using Bayesian structural time series. The concepts of non-linearity and non-stationarity, as well as methods for processing non-linearity’sand non-stationarity in the construction of forecasting models are considered. The features of the Bayesian approach in the processing of nonlinearities and nonstationaryare presented. An approach to the construction of probabilistic-statistical models based on Bayesian structural models of time series has been studied. Parametric and non-parametric methods for forecasting non-linear and non-stationary time series are considered. Parametric methods include methods: classical autoregressive models, neural networks, models of support vector machines, hidden Markov models. Non-parametric methods include methods: state-space models, functional decomposition models, Bayesian non-parametric models. One of the types of non-parametric models isBayesian structural time series. The main features of constructing structural time series are considered. Models of structural time series are presented. The process of learning the Bayesianstructural model of time series is described. Training is performed in four stages: setting the structure of the model and a priori probabilities; applying a Kalman filter to update state estimates based on observed data;application of the “spike-and-slab”method to select variables in a structural model; Bayesian averaging to combine the results to make a prediction. An algorithm for constructing a Bayesian structural time seriesmodel is presented. Various components of the BSTS model are considered andanalysed, with the help of which the structures of alternative predictive models are formed. As an example of the application of Bayesian structural time series, the problem of predicting Amazon stock prices is considered. The base dataset is amzn_share. After loading, the structure and data types were analysed, and missing values were processed. The data are characterized by irregular registration of observations, which leads to a large number of missing values and “masking” possible seasonal fluctuations. This makes the task of forecasting rather difficult. To restore gaps in the amzn_sharetime series, the linear interpolation method was used. Using a set of statistical tests (ADF, KPSS, PP), the series was tested for stationarity. The data set is divided into two parts: training and testing. The fitting of structural models of time series was performed using the Kalman filterand the Monte Carlo method according to the Markov chain scheme. To estimate and simultaneously regularize the regression coefficients, the spike-and-slab method was applied. The quality of predictive models was assessed.
The article describes a method for developing and modelling composite web-services. Web-service composition is used to derive new functionality from the interaction of existing web-services. Composite web-services are built in several stages: specifications (determining the type of service); development of the structure of the service based on the algebra of services; service composition modelling; selecting a service variant and generating a service. The main elements of the proposed approach are the algebra of services and web-services interaction models (basic and composite). The above approach formally presents the consideration of the main aspects in solving problems related to the construction of effective composite web-services and the selection of mathematical models, namely: description of web-services, determining the structure of web-services, taking into account the dynamics of information changes, taking into account the main uncertainties in building the structure web-services. Based on the approach, a method for constructing composite web-services has been developed. The method is based on an algebraic description of a web-service based on a specialized algebra of services. The method consists of the following steps: description of the task of developing a web-service; development of the structure of a web service based on the algebra of services; formal description of the structure and clarification of service operations; building models of functioning and interaction of service components; building simulation models of the composite service; defining the final structure of the composite service; web-service implementation. The main tool for describing composite services is the algebra of services, and the model building tool is colouredPetri nets implemented using СPN Tools. As an example of the application of the developed method, the construction of a pharmaceutical service is described, in which the modellingof the interaction of web-services based on Petri nets is used. The process of building a composite model of a web-service is considered. The process begins with building a pharmaceutical web-service model structure based on the service algebra. Based on the service algebra, operators were developed to implement composite services. The structure of the model is developed, which is presented in the form of a formal description. The process of building pharmaceutical service models in the СPN Tools environment is described in detail.
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