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

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 r (1) estimator, C-statistic, ordinary least squares estimator (OLS) and maximum likeli...

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Autores principales: Krone, Tanja, Albers, Casper J., Timmerman, Marieke E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5227053/
https://www.ncbi.nlm.nih.gov/pubmed/28133396
http://dx.doi.org/10.1007/s11135-015-0290-1
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author Krone, Tanja
Albers, Casper J.
Timmerman, Marieke E.
author_facet Krone, Tanja
Albers, Casper J.
Timmerman, Marieke E.
author_sort Krone, Tanja
collection PubMed
description 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 r (1) 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 r (1). 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.
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spelling pubmed-52270532017-01-25 A comparative simulation study of AR(1) estimators in short time series Krone, Tanja Albers, Casper J. Timmerman, Marieke E. Qual Quant Article 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 r (1) 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 r (1). 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. Springer Netherlands 2015-12-09 2017 /pmc/articles/PMC5227053/ /pubmed/28133396 http://dx.doi.org/10.1007/s11135-015-0290-1 Text en © The Author(s) 2015 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Krone, Tanja
Albers, Casper J.
Timmerman, Marieke E.
A comparative simulation study of AR(1) estimators in short time series
title A comparative simulation study of AR(1) estimators in short time series
title_full A comparative simulation study of AR(1) estimators in short time series
title_fullStr A comparative simulation study of AR(1) estimators in short time series
title_full_unstemmed A comparative simulation study of AR(1) estimators in short time series
title_short A comparative simulation study of AR(1) estimators in short time series
title_sort comparative simulation study of ar(1) estimators in short time series
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5227053/
https://www.ncbi.nlm.nih.gov/pubmed/28133396
http://dx.doi.org/10.1007/s11135-015-0290-1
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