Review Articles

Nonlinear prediction via Hermite transformation

Tucker McElroy ,

a U.S. Census Bureau, Washington, DC, USA

tucker.s.mcelroy@census.gov

Srinjoy Das

b University of California San Diego, La Jolla, CA, USA

Pages 49-54 | Received 25 Oct. 2019, Accepted 24 Nov. 2020, Published online: 17 Dec. 2020,
  • Abstract
  • Full Article
  • References
  • Citations

ABSTRACT

General prediction formulas involving Hermite polynomials are developed for time series expressed as a transformation of a Gaussian process. The prediction gains over linear predictors are examined numerically, demonstrating the improvement of nonlinear prediction.

References

  1. Brockett, P. L., Hinich, M. J., & Patterson, D. (1988). Bispectral-based tests for the detection of Gaussianity and linearity in time series.Journal of the American Statistical Association83(403), 657–664. https://doi.org/10.1080/01621459.1988.10478645 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  2. Brockwell, P. J., & Davis, R. A. (2013). Time series: Theory and methods. Springer Science & Business Media. [Google Scholar]
  3. Janicki, R., & McElroy, T. (2016). Hermite expansion and estimation of monotonic transformations of Gaussian data. Journal of Nonparametric Statistics28(1), 207–234. https://doi.org/10.1080/10485252.2016.1139880 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  4. Maravall, A. (1983). An application of nonlinear time series forecasting. Journal of Business & Economic Statistics1(1), 66–74. https://doi.org/10.1080/07350015.1983.10509325 [Taylor & Francis Online], [Google Scholar]
  5. McElroy, T. (2010). A nonlinear algorithm for seasonal adjustment in multiplicative component decompositions. Studies in Nonlinear Dynamics and Econometrics14(4). Article 6. https://doi.org/10.2202/1558-3708.1756 [Web of Science ®], [Google Scholar]
  6. McElroy, T. (2016). On the measurement and treatment of extremes in time series. Extremes19(3), 467–490. https://doi.org/10.1007/s10687-016-0254-4 [Crossref][Web of Science ®], [Google Scholar]
  7. McElroy, T., & McCracken, M. (2017). Multi-step ahead forecasting of vector time series. Econometric Reviews36(5), 495–513. https://doi.org/10.1080/07474938.2014.977088 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  8. McElroy, T., & Politis, D. (2020). Time series: A first course with bootstrap starter. Chapman Hall. [Google Scholar]
  9. Roman, S. (1984). The umbral calculus. Academic Press. [Google Scholar]
  10. Taniguchi, M., & Kakizawa, Y. (2000). Asymptotic theory of statistical inference for time series. Springer. [Crossref], [Google Scholar]
  11. Varma, R. S. (1951). On Appell polynomials. Proceedings of the American Mathematical Society2(4), 593–596. https://doi.org/10.1090/S0002-9939-1951-0042547-5 [Crossref][Web of Science ®], [Google Scholar]