×

zbMATH — the first resource for mathematics

Specification, estimation, and evaluation of smooth transition autoregressive models. (English) Zbl 1254.91686
Summary: We consider the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) autoregressive models. This includes the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models are discussed. Estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model. The proposed techniques are illustrated by examples using both simulated and real time series.

MSC:
91B84 Economic time series analysis
91B82 Statistical methods; economic indices and measures
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1109/TAC.1974.1100705 · Zbl 0314.62039
[2] DOI: 10.1093/biomet/77.4.669
[3] Auestad B., Nonparametric Functional Estimation and Related Topics pp 493– (1991)
[4] DOI: 10.1002/9780470316757
[5] DOI: 10.1111/j.1467-9892.1986.tb00501.x · Zbl 0596.62085
[6] DOI: 10.2307/2289548 · Zbl 0708.62053
[7] DOI: 10.2307/2335690 · Zbl 0362.62026
[8] DOI: 10.2307/1402894 · Zbl 0586.62145
[9] DOI: 10.2307/1912773 · Zbl 0491.62099
[10] DOI: 10.2307/1911409 · Zbl 0473.62106
[11] Godfrey L. G., Misspecification Tests in Econometrics (1988) · Zbl 0849.62063
[12] DOI: 10.1111/j.1467-9892.1984.tb00379.x · Zbl 0555.62071
[13] DOI: 10.1093/biomet/68.1.189 · Zbl 0462.62070
[14] Harvey A. C., The Econometric Analysis of Time Series,, 2. ed. (1990) · Zbl 0747.62113
[15] DOI: 10.1016/0165-1765(80)90024-5
[16] DOI: 10.1214/aos/1176344207 · Zbl 0383.62055
[17] DOI: 10.1080/01621459.1991.10475126
[18] Lim K. S., Journal of Time Series Analysis 8 pp 161– (1987) · Zbl 0608.62116
[19] DOI: 10.1093/biomet/65.2.297 · Zbl 0386.62079
[20] DOI: 10.1007/BF02613866 · Zbl 0107.36503
[21] Luukkonen R., On Linearity Testing and Model Estimation in Nonlinear Time Series Analysis (1990)
[22] DOI: 10.1093/biomet/75.3.491 · Zbl 0657.62109
[23] DOI: 10.1111/j.1467-9892.1983.tb00373.x · Zbl 0536.62067
[24] Ozaki T., Handbook of Statistics 5 pp 25– (1985)
[25] Priestley M. B., Non-Linear and Non-Stationary Time-Series Analysis (1988) · Zbl 0687.62072
[26] DOI: 10.1016/0005-1098(78)90005-5 · Zbl 0418.93079
[27] Saikkonen P., Scandinavian Journal of Statistics 15 pp 55– (1988)
[28] DOI: 10.1214/aos/1176344136 · Zbl 0379.62005
[29] DOI: 10.1002/0471725315
[30] DOI: 10.1002/jae.3950070509
[31] Teräsvirta T., Scandinavian Journal of Statistics 13 pp 159– (1986)
[32] DOI: 10.1111/j.1467-9892.1990.tb00043.x · Zbl 04574268
[33] DOI: 10.1016/0304-4149(86)90099-2 · Zbl 0598.62109
[34] DOI: 10.2307/2345278
[35] Tong H., Threshold Models in Non-Linear Time Series Analysis (1983) · Zbl 0527.62083
[36] Tong H., Non-Linear Time Series: A Dynamical System Approach (1990) · Zbl 0716.62085
[37] Tong H., Journal of the Royal Statistical Society 42 pp 245– (1980)
[38] DOI: 10.1093/biomet/73.2.461 · Zbl 0603.62097
[39] DOI: 10.1080/01621459.1989.10478760
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.