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Approximate sampling distribution of the serial correlation coefficient for small samples

Gary D. Tasker
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Abstract

The probability density function for the sample serial correlation coefficient r can be approximated by f ( r ) = (β(½, ½( T + 1))) −1 (1 − r 2 ) ½( T − 1 )(1+ c 2 − 2 cr ) −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.

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Gary D. Tasker. 2010-07-09. Approximate sampling distribution of the serial correlation coefficient for small samples. https://doi.org/10.1029/wr019i002p00579

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