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Autocorrelation and Bias in Short Time Series: An Alternative Estimator

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Abstract

The conventional first-order autocorrelationcoefficient r1 generates an empiricalbias when it is applied to short time series.The properties of this estimator have beenexamined with a Monte Carlo simulation studyusing the MATLAB program (version5.2). This study also analyzes the functionof the empirical bias with the polynomicregression and derives a polynomic fittingmodel for different sample sizes. In thisway, a new estimator that has been correctedby the absolute value of the fitting model(r1') is proposed. Having analyzed thestatistical properties of the estimator r1',it is shown that the empirical bias generatedby r1' is less in relationship to r1 andr1+. The results of the study make itpossible to verify that the mean squared errorassociated to the estimator r1 isless than that of r1. Thus, the coefficient r1'is recommended to estimate the lag-oneautocorrelation coefficient in samples under 50observations.

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Authors and Affiliations

  1. Department of Methodology of Behavioral Sciences, Psychology Faculty, University of Barcelona, Spain

    Jaume Arnau

  2. Department of Methodology of Behavioral Sciences, Psychology Faculty, University of Barcelona, Spain

    Roser Bono

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  1. Jaume Arnau
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  2. Roser Bono
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Arnau, J., Bono, R. Autocorrelation and Bias in Short Time Series: An Alternative Estimator. Quality & Quantity 35, 365–387 (2001). https://doi.org/10.1023/A:1012223430234

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