Speed of Convergence to Normality When Regressors Are Nonstationary

Lukasz T. Gatarek and Aleksander Welfe

Oxford Bulletin of Economics and Statistics, 2025, vol. 87, issue 5, 871-879

Abstract: Stochastic and deterministic trends always coexist in data generating processes, which causes the nonstationarity and non‐standard distributions of statistics used in inference. It is known that the presence of the deterministic trend leads to asymptotic normality of the t‐statistics. This article goes further and points out that the convergence rate depends on the share of the deterministic trend in the data generating process, which can be assessed from the estimator derived in the article. This finding is of significance for empirical research, because it shows that in the case of two samples of the same relatively small size, the one with dominance of the deterministic trend may satisfy asymptotic properties, enabling the use of standard approach, whereas the other one requires different strategy of statistical inference.

Date: 2025
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