Estimation of the Mean and the Autocorrelation Function

Klaus Neusser ()

Chapter 4 in Time Series Econometrics, 2016, pp 67-85 from Springer

Abstract: Abstract In the previous chapters we have seen in which way the mean μ, and, more importantly, the autocovariance function, γ(h), h = 0, ±1, ±2, …, of a stationary stochastic process {X t } characterize its dynamic properties, at least if we restrict ourself to the first two moments. In particular, we have investigated how the autocovariance function is related to the coefficients of the corresponding ARMA process. Thus the estimation of the ACF is not only interesting for its own sake, but also for the specification and identification of appropriate ARMA models. It is therefore of outmost importance to have reliable (consistent) estimators for these entities. Moreover, we want to test specific features for a given time series. This means that we have to develop corresponding testing theory. As the small sample distributions are hard to get, we rely for this purpose on asymptotic theory.

Keywords: Kernel Function; Autocorrelation Function; ARMA Model; Autocovariance Function; Stationary Stochastic Process (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-319-32862-1_4

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DOI: 10.1007/978-3-319-32862-1_4

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