A method of combining three analytic techniques including regression rule induction, the k-nearest neighbors method and time series forecasting by means of the ARIMA methodology is presented. A decrease in the forecasting error while solving problems that concern natural hazards and machinery monitoring in coal mines was the main objective of the combined application of these techniques. The M5 algorithm was applied as a basic method of developing prediction models. In spite of an intensive development of regression rule induction algorithms and fuzzy-neural systems, the M5 algorithm is still characterized by the generalization ability and unbeatable time of data model creation competitive with other systems. In the paper, two solutions designed to decrease the mean square error of the obtained rules are presented. One consists in introducing into a set of conditional variables the so-called meta-variable (an analogy to constructive induction) whose values are determined by an autoregressive or the ARIMA model. The other shows that limitation of a data set on which the M5 algorithm operates by the k-nearest neighbor method can also lead to error decreasing. Moreover, three application examples of the presented solutions for data collected by systems of natural hazards and machinery monitoring in coal mines are described. In Appendix, results of several benchmark data sets analyses are given as a supplement of the presented results.
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