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H ασυμπτωτική διακύμανση στην εκτίμηση του στάσιμου μέσου υπό συνθήκες αυτοσυσχέτισης

George, Halkos and Ilias, Kevork (2004): H ασυμπτωτική διακύμανση στην εκτίμηση του στάσιμου μέσου υπό συνθήκες αυτοσυσχέτισης.

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Abstract

In this study, using Monte Carlo simulations, we evaluate three alternative methods for constructing confidence intervals for the population mean in the case of a stationary first order autoregressive process, AR(1), with parameter . Differentiating the three methodologies with respect to the way of estimating the asymptotic variance, we infer that in constructing confidence intervals we have to avoid the use of the observations of the time series under consideration for the estimation of the autovariance and the autocorrelation coefficients. Instead, it is preferable to identify the series according to Box-Jenkins and then use the asymptotic variance derived from the corresponding ARMA model after the substitution of the OLS parameter and error variance estimates. It is worth mentioning that using the asymptotic variance, for small samples and in the case of an AR(1) with positive  values, the expected actual confidence levels are larger as compared to the corresponding nominal ones, indicating a potential area for future research.

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