title: A comparative simulation study of AR(1) estimators in short time series.
abstract: 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 frequentistr1estimator, C-statistic, ordinary least squares estimator (OLS) and maximum likelihood estimator (MLE), and a Bayesian method, considering flat (Bf) and symmetrized reference (Bsr) 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 Bsr, and a lowest variability forr1. The power in different conditions is highest for Bsrand OLS. ForT= 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., Bsrand 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.
authors.affiliation: Heymans Institute for Psychological Research, Psychometrics and Statistics, Grote Kruisstraat 2/1, 9712TS Groningen, The Netherlands.
authors.forename: Tanja
authors.identifier: 0000-0003-4902-9907
authors.initials: T
authors.lastname: Krone
authors.affiliation: Heymans Institute for Psychological Research, Psychometrics and Statistics, Grote Kruisstraat 2/1, 9712TS Groningen, The Netherlands.
authors.forename: Casper J
authors.initials: CJ
authors.lastname: Albers
authors.affiliation: Heymans Institute for Psychological Research, Psychometrics and Statistics, Grote Kruisstraat 2/1, 9712TS Groningen, The Netherlands.
authors.forename: Marieke E
authors.initials: ME
authors.lastname: Timmerman
keywords: AR(1); Autocorrelation; Bayesian MCMC; Misspecification; Time series analysis