Methods for Forecasting Nonlinear Non-stationary Processes in Machine Learning

Bidyuk, Petro I.; Gozhyj, Aleksandr; Калініна, Ірина; Vysotska, Victoria

doi:10.1007/978-3-030-61656-4_32

Cited by 7 publications

(5 citation statements)

References 17 publications

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“…Various non-linear and non-stationary time series forecasting methods presented in the literature are considered and classified based on how they are applied to predict time series data for real-world problems [1,2], [3,8], [9,10], [11,12]. Prediction methods can be classified based on prerequisites or approaches to overcome non-stationarity and nonlinearity, as they assume the following features: a known trend shape, piecewise stationarity of signals, progressively varying parameters, or decomposability of a signal into stationary segments in the transformed domain, and they are either parametric or non-parametric, depending on whether the predictor takes a certain form or is built solely in accordance with the data (for example, the number of latent variables may vary).…”

Section: Analysis Of Literary Datamentioning

confidence: 99%

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Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series

Kalinina¹,

Gozhyj²

2022

AAIT

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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.

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Section: Analysis Of Literary Datamentioning

confidence: 99%

“…Forecasting of complex systems is one of the important areas of modern science of data analysis and processing [1,2], [3]. One of the most developed and researched areas is forecasting based on time series.…”

Section: Introductionmentioning

confidence: 99%

Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series

Kalinina¹,

Gozhyj²

2022

AAIT

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“…If the filling of gaps is performed using a regression model, for example, AR(p), it makes sense to analyze the quality of the model, which will be built on a sample of filled gaps [4][5][6]. To do this, it is possible to use the following criterion:…”

Section: Fig 9 Distribution Of a Discrete Variable Before And After Filling In The Gapsmentioning

confidence: 99%

An Approach to Identifying and Filling Data Gaps in Machine Learning Procedures

Bidyuk

Калініна

Gozhyj

2021

Lecture Notes in Computational Intelligence and Decision Making

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The article considers the methods of detecting and filling gaps in data sets at the stage of preliminary data processing in machine learning procedures. A multi-stage approach to identifying and filling gaps in data sets and combined statistical quality criteria is proposed. The method consists of three stages. At the first stage, the presence of gaps in the data is determined. In the second stage, the patterns of occurrence of gaps are investigated. Three approaches are used: matrix analysis, graphical analysis and correlation analysis. One of the mechanisms of formation of gaps in the data is identified: MCAR, MAR, MNAR. In the third stage, various methods of data generation without gaps are used. The methods used include deleting part of the data with gaps, various replacement methods, methods for predicting missing values. Consider separately the methods of overcoming gaps in time series. The effectiveness of the proposed approach is investigated numerically. Examples of application of methods on various data sets are given.

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“…Каппа -це показник, який порівнює спостережувану точність з очікуваною точністю (випадковий шанс). Формальне визначення F-заходи і Каппи [14]:…”

Section: застосування розробленої методології класифікаціїunclassified

“…Відгук -це міра повноти, яка являє собою співвідношення між кількістю правильно прогнозованих значень і загальною кількістю релевантних значень. Вони розраховуються з використанням значень істинно позитивної швидкості, непозитивної швидкості і помилково негативної швидкості в результатах прогнозування.Робоча характеристика приймача (ROC)[14] може використовуватися як ще одна метрика, яка також включає частоту справжніх позитивних і помилкових спрацьовувань для оцінки якості вихідних даних класифікатора. Якщо TP, FP і FN позначають справжні спрацьовування, помилкові спрацьовування і помилкові заперечення, то формальне визначення точності і відкликання буде[14]: -точність;  -відгук.…”

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Study of the Efficiency of Classification Methods in Forecasting in Machine Learning Tasks

Калініна¹,

Гожий²

2021

MDCS

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The article considers the use of classification methods to solve the problem of predicting the aerodynamic properties of materials. The methodology of classification by methods of machine learning is offered and investigated. The following logistic regression (LR), K-nearest neighbors (KNN) method, decision trees (DT) and random forest (RF) were used as classification methods. The methodology consists of the following stages: data collection, exploratory data analysis, modeling, evaluation of model efficiency, and improving model efficiency. To implement the forecasting procedure, preliminary data processing was performed, which consists of stages: Data collection and Intelligence data analysis. The next stage – Modeling, consists of two parts: Preparation and Selection of the model. The accuracy of forecasts is calculated. The analysis examined the prediction results in terms of accuracy, such as response, F-measure, Kappa, performance value (ROC) and error rate measured by the mean absolute error (MAE) and the root mean square error (RMSE). The analysis of forecasting accuracy is carried out.

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Methods for Forecasting Nonlinear Non-stationary Processes in Machine Learning

Cited by 7 publications

References 17 publications

Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series

Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series

An Approach to Identifying and Filling Data Gaps in Machine Learning Procedures

Study of the Efficiency of Classification Methods in Forecasting in Machine Learning Tasks

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