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Statistical analyses in economics are often based on explaining the phenomena by comparing time series. The purpose of such types of analyses is to find out the similarity and schematic behavior of phenomena which appear in the data. Usual time series are compared with the use of a different similarity measure which, in accordance with the literature, could be divided into four categories. In this article, I propose a method that allows to indicate whether two time series are generated by the same stochastic processes. For this purpose, I analyze a method based on a permutation test. The idea of this test is much simpler than the tests based on theoretical distributions. I also conducted a simulation analysis based on the data generated according to different scenarios, subsequently comparing the results of that analysis.
PL
W artykule przedstawiono propozycję testu pozwalającego wykryć pierwiastki jednostkowe w szeregach czasowych z autoregresją. Proponowane rozwiązanie odwołuje się do testu pierwiastków jednostkowych Akdi-Dickeya, który opiera się na analizie spektralnej szeregu czasowego. W tym celu wykorzystywany jest periodogram szeregu czasowego, tworzony poprzez transformację zmiennej yt w dziedzinę czasu. Proponowane rozwiązanie zostało porównane symulacyjnie z innymi testami pierwiastków jednostkowych znanymi z literatury.
EN
In this paper, a proposal of test to detect unit root in the time series from the process with autoregression was presented. The proposed solution refers to the Akdi- -Dickey unit root test which is based on the spectral time series analysis. The basis of the test is to analyze the periodogram of series obtained by the transformation of the yt variable into the field of the frequency. The proposed modification uses a permutation test which specificity allows us to take general assumptions. The proposed solution was compared using a computer simulation with the solutions known from the literature.
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