CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
The method of time series forecasting groups using algorithms of cluster analysis
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Read | Astakhova Nadezhda N., Demidova Liliya A. The method of time series forecasting groups using algorithms of cluster analysis // Caspian journal : management and high technologies. — 2015. — №2. — pp. 59-79. |
Astakhova Nadezhda N. - post-graduate student, Ryazan State Radio Engineering University, 59/1 Gagarin Str., Ryazan, 390005, Russian Federation, asnadya@yandex.ru
Demidova Liliya A. - D.Sc. (Engineering), Professor, Ryazan State Radio Engineering University, 59/1 Gagarin Str., Ryazan, 390005, Russian Federation, liliya.demidova@rambler.ru
The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. K-means algorithm is suggested to be a basic one for clustering. In order to estimate the distance between time series a metric has been introduced. It allows to take into account the relevance of the time series elements in different time during the clustering. It is supposed to group time series into clusters (subgroups), using time series values of the elements as characteristic values. On the basis of such data the clustering algorithm makes a decision to classify the time series to a particular cluster. The coordinates of the centers of clusters have been put in correspondence with summarizing time series data - the centroids of the clusters. A description of time series, the centroids of the clusters, is implemented with the use of predictive models. They are based on strict binary trees and a modified clonal selection algorithm. With the help of such predictive models, the possibility of forming analytic dependences is shown. The last-mentioned describes acquainted values of time series in the best way and provides minimum values of the average relative error of prediction. It is suggested to use a common prediction model, which is constructed for time series - the centroid of the cluster, in predicting the private (individual) time series in the cluster. The conclusion about the possibility of obtaining individual results of time series prediction is made by using the values of the elements of private time series as values of the variables in the general prediction models. The promising application of the suggested method for grouped time series forecasting is demonstrated.
Key words: временной ряд, кластеризация, центроид кластера, алгоритм четких с-средних, модель прогнозирования, средняя относительная ошибка прогнозирования, строго бинарное дерево, антитело, антиген, модифицированный алгоритм клонального отбора, time series, cluster