Asymptotic relationship between sample mean and sample variance for autoregressive processes of order 1

Autoregressive processes of order 1 (or AR(1) processes) have been extensively used in econometrics and time series literature. Noting that an early important result concerning the sample mean ?? and variance ?? of independent normally distributed random variables ?? with equal means and variances i...

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Bibliographic Details
Published inJournal of Statistical and Econometric Methods Vol. 6; no. 1
Main Author Polymenis, Athanase
Format Journal Article
LanguageEnglish
Published Christchurch Scientific Press International Limited 01.01.2017
Subjects
Random variables
Sample variance
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Summary:Autoregressive processes of order 1 (or AR(1) processes) have been extensively used in econometrics and time series literature. Noting that an early important result concerning the sample mean ?? and variance ?? of independent normally distributed random variables ?? with equal means and variances is that ?? and ?? are independent, the present article investigates whether this result can be extended to AR(1) non-stationary processes as the sample size becomes very large. To this end, a property called “asymptotic stationarity” is used for algebraic calculations. A result for asymptotic independence concerning the sample mean and variance is then adequately derived for these types of processes. Mathematics Subject Classification: 62E20; 62M10
Bibliography:ObjectType-Article-1
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ISSN:2241-0384
2241-0376