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

Quality and Quantity

Volumn 51, Issue 1, 2017, Pages 1-21

  Krone, Tanja ^a   Albers, Casper J ^a   Timmerman, Marieke E ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

AR(1); Autocorrelation; Bayesian MCMC; Misspecification; Time series analysis

Indexed keywords

EID: 84949523140     PISSN: 00335177     EISSN: 15737845     Source Type: Journal    
DOI: 10.1007/s11135-015-0290-1     Document Type: Article

References (28)

1. Arnau, J., Bono, R.: Autocorrelation and bias in short time series: an alternative estimator. Qual. Quant. 35(4), 365–387 (2001). doi:10.1023/A:1012223430234
2. Berger, J.O., Yang, R.Y.: Noninformative priors and Bayesian testing for the AR(1) model. Econ. Theory 10, 461–482 (1994). doi:10.1017/S026646660000863X
3. Box, G.E.P., Jenkins, G.M.: Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco (1976)
4. Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995). doi:10.1137/0916069
5. Cox, D.D., Llatas, I.: Maximum likelihood type estimation for nearly nonstationary autoregressive time series. Ann. Stat. 19(3), 1109–1128 (1991). doi:10.1214/aos/1176348240
6. DeCarlo, L.T., Tryon, W.W.: Estimating and testing autocorrelation with small samples: a comparison of the C-statistic to a modified estimator. Behav. Res. Ther. 31(8), 781–788 (1993). doi:10.1016/0005-7967(93)90009-J
7. Durbin, J., Koopman, S.: Time Series Analysis by State Space Models. Oxford University Press, Oxford (2012)
8. Garcia-Hiernaux, A., Casals, J., Jerez, M.: Fast estimation methods for time-series models in state-space form. J. Stat. Comput. Simul. 79(2), 121–134 (2009). doi:10.1080/00949650701617249
9. Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Stat. Sci. 7(4), 457–472 (1992). doi:10.1214/ss/1177011136
10. Huitema, B.E., McKean, J.W.: Autocorrelation estimation and inference with small samples. Psychol. Bull. 110(2), 291–304 (1991). doi:10.1037/0033-2909.110.2.291
11. Huitema, B.E., McKean, J.W.: Reduced bias autocorrelation estimation: three jackknife methods. Educ. Psychol. Meas. 54(3), 654 (1994). doi:10.1177/0013164494054003008
12. Kendall, S.M., Ord, J.K.: Time Series. Edward Arnold, London (1990)
13. Kunitomo, N., Yamamoto, T.: Properties of predictors in misspecified autoregressive time series models. J. Am. Stat. Assoc. 80(392), 941 (1985). doi:10.1080/01621459.1985.10478208
14. Lütkepohl, H.: Introduction to Multiple Time Series Analysis. Springer Verlag, Berlin (1991)
15. Pantula, S.G., Fuller, W.A.: Mean estimation bias in least squares estimation of autoregressive processes. J. Econ. 77(1), 99–121 (1985). doi:10.1016/0304-4076(85)90046-6
16. Price, L.R.: Small sample properties of bayesian multivariate autoregressive time series models. Struct. Equ. Model. 19(1), 51–64 (2012). doi:10.1080/10705511.2012.634712
17. R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, URL http://www.R-project.org/
18. Solanas, A., Manolov, R., Sierra, V.: Lag-one autocorrelation in short series: estimation and hypotheses testing. Psicologica 31(2), 357–381 (2010)
19. Stan Development Team (2014) RStan: the R interface to Stan, version 2.4. URL http://mc-stan.org/rstan.html
20. Stoica, P., Friedlander, B., Söderström, T.: Least-squares, yule-walker, and overdetermined walker estimation of ar parameters: a Monte Carlo analysis of finite-sample properties. Int. J. Control 43(1), 13–27 (1986). doi:10.1080/00207178608933446
21. Tanaka K (1984) An asymptotic expansion associated with the maximum likelihood estimators in ARMA models. J. R. Stat. Soc. Ser. B Methodol. 46(1):58–67. URL http://www.jstor.org/stable/2345462
22. Tanaka, K., Maekawa, K.: The sampling distributions of the predictor for an autoregressive model under misspecifications. J. Econ. 25(3), 327–351 (1984). doi:10.1016/0304-4076(84)90005-8
23. Walker, G.: On periodicity in series of related terms. Proc. R. Soc. Lon. Ser. A Contain. Pap. Math. Phys. Character 131(818), 518–532 (1931). doi:10.1098/rspa.1931.0069
24. Watson P, Nicholls S (1992) ARIMA modelling in short data sets: some Monte Carlo results. Soc. Econ. Stud. 41(4):53–75. URL http://www.jstor.org/stable/27865115
25. West, K.D., Wilcox, D.W.: A comparison of alternative instrumental variables estimators of a dynamic linear model. J. Bus. Econ. Stat. 14(3), 281–293 (1996). doi:10.2307/1392443
26. Young, L.: On randomness in ordered sequences. Ann. Math. Stat. 12(3), 293–300 (1941). doi:10.1214/aoms/1177731711
27. Yule, G.U.: On a method of investigating periodicities in disturbed series, with special reference to Wolfer’s sunspot numbers. Philos. Trans. R. Soc. Lon. Ser. A Contain. Pap. Math. Phys. Character 226, 267–298 (1927). doi:10.1098/rsta.1927.0007
28. Zhang, Z., Nesselroade, J.R.: Bayesian estimation of categorical dynamic factor models. Multivar. Behav. Res. 42(4), 729–756 (2007). doi:10.1080/00273170701715998