A comparative simulation study of AR(1) estimators in short time series

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• 作者：Tanja Krone ; Casper J. Albers ; Marieke E. Timmerman
• 关键词：Time series analysis ; Autocorrelation ; AR(1) ; Bayesian MCMC ; Misspecification
• 刊名：Quality & Quantity
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：51
• 期：1
• 页码：1-21
• 全文大小：1337KB
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Methodology of the Social Sciences; Social Sciences, general;
• 出版者：Springer Netherlands
• ISSN：1573-7845
• 卷排序：51

文摘

Various estimators of the autoregressive model exist. We compare their performance in estimating the autocorrelation in short time series. In Study 1, under correct model specification, we compare the frequentist r₁ estimator, C-statistic, ordinary least squares estimator (OLS) and maximum likelihood estimator (MLE), and a Bayesian method, considering flat (B_f) and symmetrized reference (B_sr) priors. In a completely crossed experimental design we vary lengths of time series (i.e., T = 10, 25, 40, 50 and 100) and autocorrelation (from −0.90 to 0.90 with steps of 0.10). The results show a lowest bias for the B_sr, and a lowest variability for r₁. The power in different conditions is highest for B_sr and OLS. For T = 10, the absolute performance of all measurements is poor, as expected. In Study 2, we study robustness of the methods through misspecification by generating the data according to an ARMA(1,1) model, but still analysing the data with an AR(1) model. We use the two methods with the lowest bias for this study, i.e., B_sr and MLE. The bias gets larger when the non-modelled moving average parameter becomes larger. Both the variability and power show dependency on the non-modelled parameter. The differences between the two estimation methods are negligible for all measurements.