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

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  • Athanase Polymenis

Abstract

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 𝑈 and variance 𝑆 of independent normally distributed random variables 𝑈 with equal means and variances is that 𝑈 and 𝑆 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; 62M10Keywords: Autoregressive process; Asymptotic stationarity; Asymptotic independence

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  • Athanase Polymenis, 2017. "Asymptotic relationship between sample mean and sample variance for autoregressive processes of order 1," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-4.
    • Handle: RePEc:spt:stecon:v:6:y:2017:i:1:f:6_1_4
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    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. Spanos,Aris, 1986. "Statistical Foundations of Econometric Modelling," Cambridge Books, Cambridge University Press, number 9780521269124.
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