Systems and Means of Informatics

2026, Volume 36, Issue 2, pp 106-115

IMPLEMENTING UNIT ROOT TESTS FOR SMALL SAMPLES

  • M. P. Krivenko

Abstract

The criteria of the unit root are widely used in the analysis of the stationarity of a time series. There is a detailed substantiation of the variants of such tests which in mathematical statistics are called the Dickey-Fuller criteria.
The efficacy of the proposed methods for describing the limiting distributions of the statistics used has been confirmed in the course of many studies but they turned out to be unproductive at the finite values of the observation time T. Therefore, it was necessary to turn to the method of statistical trials (MST), with the help of which percentile tables were constructed for individual T values. In addition to the fact that they were clearly insufficient, in fact, for the convenience of using preconstructed statistical tables, the researcher was forced to turn to a simple data model in conjunction with a fixed set of artificially selected competing hypotheses. As a result, the only solution to the problem of applying the unit root criteria for small T in practice is the use of MST. Earlier, the author of this article considered the use of cointegration analysis in the ranking of a set of objects on the basis of a single indicator - the degree of connectivity of the components of the observed multidimensional time series.
The newly constructed statistical tables for T = 8 made it possible to confirm the correctness of the replacement of the unit root criteria due to small T with the stationarity criteria of a general nature. The capabilities of modern processors that allow multitasking as well as the prospects for using the R platform speak in favor of the productivity of simulation in the practice of data analysis.

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