Autoregressive Approximation in Nonstandard Situations: The Non-Invertible and Fractionally Integrated Cases

Donald Poskitt

No 16/05, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Autoregressive models are commonly employed to analyze empirical time series. In practice, however, any autoregressive model will only be an approximation to reality and in order to achieve a reasonable approximation and allow for full generality the order of the autoregression, h say, must be allowed to go to infinity with T, the sample size. Although results are available on the estimation of autoregressive models when h increases indefinitely with T such results are usually predicated on assumptions that exclude (i) non-invertible processes and (ii) fractionally integrated processes. In this paper we will investigate the consequences of fitting long autoregressions under regularity conditions that allow for these two situations and where an infinite autoregressive representation of the process need not exist. Uniform convergence rates for the sample autocovariances are derived and corresponding convergence rates for the estimates of AR(h) approximations are established. A central limit theorem for the coefficient estimates is also obtained. An extension of a result on the predictive optimality of AIC to fractional and non-invertible processes is obtained.

Keywords: Autoregression; Autoregressive approximation; Fractional process; Non-invertibility; Order selection; Asymptotic efficiency. (search for similar items in EconPapers)
JEL-codes: C14 C32 C53 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2005-06
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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