Confidence intervals with higher accuracy for short and long-memory linear processes

Masoud M. Nasari () and Mohamedou Ould-Haye ()
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Masoud M. Nasari: School of Mathematics and Statistics
Mohamedou Ould-Haye: School of Mathematics and Statistics

Statistical Papers, 2022, vol. 63, issue 4, No 8, 1187-1220

Abstract: Abstract In this paper an easy to implement method of stochastically weighing short and long-memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly more accurate than their classic counterparts for each fixed sample size n. It is illustrated both theoretically and numerically that the randomization framework of this paper produces randomized (asymptotic) pivotal quantities, for the mean, which admit central limit theorems with smaller magnitudes of error as compared to those of their leading classic counterparts. An Edgeworth expansion result for randomly weighted linear processes whose innovations do not necessarily satisfy the Cramer condition, is established. Numerical illustrations and applications to real world data are also included.

Keywords: Accuracy of the CLT; Confidence intervals; Limit theorems; Edgeworth expansion; Linear processes; Long memory; Time series analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01265-w

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