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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, September.
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