A comparative study of parametric and semiparametric autoregressive models

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    Dynamic linear regression models are used widely in applied econometric research. Most applications employ linear autoregressive (AR) models, distributed lag (DL) models or autoregressive distributed lag (ARDL) models. These models, however, perform poorly for data sets with unknown, complex nonlinear patterns. This paper studies nonlinear and semiparametric extensions of the dynamic linear regression model and explores the autoregressive (AR) extensions of two semiparametric techniques to allow unknown forms of nonlinearities in the regression function. The autoregressive GAM (GAM-AR) and autoregressive multivariate adaptive regression splines (MARS-AR) studied in the paper automatically discover and incorporate nonlinearities in autoregressive (AR) models.  Performance comparisons among these semiparametric AR models and the linear AR model are carried out via their application to Australian data on growth in GDP and unemployment using RMSE and GCV measures.

     

     


  • Keywords


    Autoregressive (AR) Models; Semiparametric Autoregressive Models; Autoregressive Generalized Additive Models (GAM-AR)); Autoregressive Multivariate Adaptive Regression Splines (MARS-AR).

  • References


      [1] Boehmke, B. and Greenwell B. (2020). Hands-on Machine Learning with R, CRC Press, Boca Raton, FL. https://doi.org/10.1201/9780367816377.

      [2] Chen, R. & Tsay, R. S. (1993). Nonlinear additive ARX models. Journal of the American Statistical Association, 88(423), 955-967. https://doi.org/10.1080/01621459.1993.10476363.

      [3] De Goojer J. A., Ray B. K. & Krager H. (1998). Forecasting exchange rates using TSMARS, J. of Int. Money and Finance, 17(3), 513-534. https://doi.org/10.1016/S0261-5606(98)00017-5.

      [4] Friedman, J. H. (1991). "Multivariate Adaptive Regression Splines". The Annals of Statistics. 19(1), 1–67. https://doi.org/10.1214/aos/1176347963.

      [5] Hardle, W., Lutkepohl H. & R. Chen (1997). A Review of Nonparametric Time Series Analysis, International Statistical Review / Revue Internationale de Statistique, 65(1), 49-72 https://doi.org/10.2307/1403432.

      [6] Hastie, T., Tibshirani, R. (1990). Generalized Additive Models, Chapman and Hall, London

      [7] Hill, R.C., Griffiths, W. E. & Lim, G. 2018, Principles of Econometrics, John Wiley & Sons, New York.

      [8] Jones, D. A. (1978). Non-linear autoregressive processes. Journal of the Royal Statistical Society, Series A, 360, 71-95. https://doi.org/10.1098/rspa.1978.0058.

      [9] Keogh, G. (2015). Is the annual growth rate in Ireland’s balance of trade time series nonlinear? https://arxiv.org/abs/1705.10510v1

      [10] Lewis P. A. W. & Ray B. K. (1997), Modelling Long-Range Dependence, Nonlinearity and Periodic Phenomena in Sea surface Temperatures using TSMARS, Journal of the American Statistical Association, 92(4), 881-893. https://doi.org/10.1080/01621459.1997.10474043.

      [11] Lewis P. A. W. & Stevens J. G. (1991). Nonlinear modelling of time series using Multivariate Adaptive Regression Splines (MARS), Journal of the American Statistical Association, 86, 864-877. https://doi.org/10.1080/01621459.1991.10475126.

      [12] Milborrow, S. (2018). Notes on the earth package, available at https://CRAN.R-project.org/package=earth.

      [13] Wood, Simon (2017). Generalized Additive Models: An Introduction with R, Chapman & Hall/CRC, Boca Raton.

      [14] Wood, Simon (2021), R package “mgcv” available at https://cran.rproject.org/web/packages/mgcv/mgcv.pdf.


 

View

Download

Article ID: 31978
 
DOI: 10.14419/ijaes.v10i1.31978




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.