Tests of Hypotheses in the Linear Autoregressive Model: II. Null Distributions for Higher Order Schemes: Non-Null Distributions

Biometrika (Impact Factor: 1.42). 06/1956; 43(1/2). DOI: 10.1093/biomet/43.1-2.186
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    ABSTRACT: This paper considers the estimation of the first—order autoregressive scheme when the underlying distribution is non—normal stable. The results of a simulation experiment of the least—squares estimator and the uncorrected and corrected serial correlation coefficients are presented. It is found that, in general, normal theory results are inapplicable. Nevertheless, the corrected coefficient provides a reliable and very efficient estimator of ρ; however, the least—squares estimator and the uncorrected coefficient are severely biased with skewed populations. Furthermore, all of the estimators seem to be asymptotically non—normal.
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    ABSTRACT: Monte Carlo methods are used to investigate the relationship between the power of different pretests for autocorrelation, and the Type I error and power of the significance test for a resulting two-stage estimate of the slope parameter in a simple regression. Our results suggest it may be preferable to always transform without pretesting. Moreover we find little room for improvement in the Type I errors and power of two-stage estimators using existing pretests for autocorrelation, compared with the results obtained given perfect knowledge about when to transform (i.e., given a perfect pretest). Rather, researchers should seek better estimators of the transformation parameter itself.
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    ABSTRACT: The probability density function for the sample serial correlation coefficient r can be approximated byf(r) = (β(½, ½(T + 1)))−1(1 − r2)½(T− 1)(1+ c2 − 2cr)−½(T), whereβ is the Beta function, T = n− 2, c = ρ − [(1 + ρ)/(n − 3)], n is the number of observations, and ρ is the population lag one serial correlation. This distribution is derived from a large Monte Carlo study at points between ρ= −0.9 and ρ = 0.9 and for n =10, 20, and 30.
    Water Resources Research 04/1983; 19(2):579-582. DOI:10.1029/WR019i002p00579 · 3.55 Impact Factor
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