Zastosowanie metody najbliższych sąsiadów do redukcji szumu losowego w ekonomicznych szeregach czasowych
The Application of the Method of Nearest Neighbours to Reduce Random Noise in an Economic Time Series

Summary/Abstract: The real time series (xt) can be written in an additive form, as: xt = yt + εt, where (yt) denotes the deterministic part of the series, and (εt) the stochastic part, which is associated with the presence of random noise in the time series, representing the observational noise, system noise, or a combination thereof. The reduction of random noise allows the properties of the series (yt) to be known based on analysis of series (xt). The nearest neighbours method is derived from the theory of nonlinear dynamic systems and was developed to predict the time series, but it can also be used to reduce noise. Here the time series (yt) is built on the basis of the nearest neighbours of vectors xtm of a reconstructed state space dynamic system, which is described with the use of the time series (xt). In this paper, the nearest neighbours method is used to reduce random noise in an economic time series. Empirical studies are conducted based on actual data of an economic nature.

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