A FORECASTING METHOD BASED ON CLUSTERING THE POLYNOMIAL EXTRAPOLATION SEQUENCE

Abstract

Time series forecasting is an important task in intelligent data analysis, especially under conditions of short samples, local non-stationarity, noise, and increased sensitivity to external disturbances. These properties are characteristic, in particular, of financial time series, where local trends, random fluctuations, and abrupt changes in dynamics may coexist even over small observation intervals. One of the promising approaches to short-term forecasting is polynomial extrapolation. However, the use of polynomials of different orders for the same segment of a series produces a set of alternative forecast values, which complicates the selection of the final forecast.

This paper proposes a short-term forecasting method based on clustering the values of the polynomial prediction sequence. For a local fragment of a time series, a sequence of polynomial forecasts  is formed over a range of polynomial orders, after which cluster analysis is applied to this set of values. The densest interval method and the DBSCAN algorithm are used to identify the dominant forecast region, while the final forecast value is defined as the central characteristic of the detected cluster. The efficiency of the proposed approach is compared with the forecasting method based on averaging the polynomial extrapolation sequence.

Experimental studies were carried out on deterministic functions, stochastic sequences, and real intraday stock data for Netflix using the Close parameter. It was found that the polynomial prediction sequence has an internal structure in the form of local extrema, concentration intervals, and distant values, which justifies the feasibility of its clustering. The scientific novelty of the study lies in refining the mechanism for selecting PPS elements by moving from index-based averaging to structural analysis of the spatial grouping of forecast values. The practical significance of the work lies in improving the robustness of short-term forecasting for financial time series.