CENTRAL LIMIT THEOREM FOR WEAKLY DEPENDENT ECONOMIC TIME SERIES: EXTENSIONS, ERROR BOUNDS, AND APPLICATION TO GDP CONFIDENCE INTERVALS

Authors

  • Mamurov I. Department of Higher and Applied Mathematics, Tashkent State University of Economics, Tashkent, Uzbekistan

DOI:

https://doi.org/10.55640/

Keywords:

central limit theorem, weak dependence, mixing conditions, long-run variance, Berry–Esseen bound, GDP confidence intervals, time series econometrics.

Abstract

This paper develops a unified probabilistic framework that extends the Classical Central Limit Theorem (CLT) to weakly dependent economic time series exhibiting autocovariance structure. The scientific novelty consists in three contributions: (i) an explicit Berry–Esseen-type bound on the normal approximation error for  sequences of the form ; (ii) a long-run variance estimator with a data-adaptive Bartlett–Newey–West kernel and a novel rate-optimal bandwidth selector; (iii) a constructive algorithm for building asymptotically exact GDP confidence intervals under dependent growth-rate innovations, validated on Uzbekistan quarterly national accounts data 2000–2023. All key results are proved rigorously and verified numerically.

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References

1. Hamilton J.D. Time Series Analysis. — Princeton: Princeton University Press, 1994. — 799 p.

2. Sims C.A. Macroeconomics and reality // Econometrica. 1980. Vol. 48. No. 1. P. 1–48.

3. Newey W.K., West K.D. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix // Econometrica. 1987. Vol. 55. No. 3. P. 703–708.

4. Andrews D.W.K. Heteroskedasticity and autocorrelation consistent covariance matrix estimation // Econometrica. 1991. Vol. 59. No. 3. P. 817–858.

5. Billingsley P. Convergence of Probability Measures. 2nd ed. — New York: Wiley, 1999. — 296 p.

6. Rio E. Théorie asymptotique des processus aléatoires faiblement dépendants. — Paris: Springer, 2000. — 169 p.

7. Ibragimov I.A., Linnik Yu.V. Independent and Stationary Sequences of Random Variables. — Groningen: Wolters-Noordhoff, 1971.

8. Hall P., Heyde C.C. Martingale Limit Theory and Its Application. — New York: Academic Press, 1980.

9. Phillips P.C.B., Solo V. Asymptotics for linear processes // Annals of Statistics. 1992. Vol. 20. No. 2. P. 971–1001.

10. Lahiri S.N. Resampling Methods for Dependent Data. — New York: Springer, 2003. — 374 p.

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Published

2026-06-10

Issue

Vol. 5 No. 6 (2026): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

CENTRAL LIMIT THEOREM FOR WEAKLY DEPENDENT ECONOMIC TIME SERIES: EXTENSIONS, ERROR BOUNDS, AND APPLICATION TO GDP CONFIDENCE INTERVALS. (2026). Journal of Multidisciplinary Sciences and Innovations, 5(6), 607-613. https://doi.org/10.55640/

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