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Model Selection in Harmonic Non-Linear Regression

In: Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach

Author

Listed:
  • Dominique Haughton

    (Bentley College, Department of Mathematical Sciences)

  • Jonathan Haughton

    (Northeastern University, Department of Economics)

  • Alan Izenman

    (Temple University, Department of Statistics)

Abstract

Summary In this paper we are concerned with the twin problems of fitting a harmonic model to a time series, and then using information criteria to determine how many harmonic components to include in the series. Let Y(t), t = 0, ±1, ±2,… be a time series. A harmonic model has the form 7.1 $$ Y(t) = {\alpha_0} + \sum\limits_{{j = 1}}^k {{\alpha_j}\;\cos \left( {2\pi {f_j}t} \right) + {\beta_j}\;\sin \left( {2\pi {f_j}t} \right) + \varepsilon (t)} $$ where the errors ɛ(t) are assumed here to be iid N(0, σ2). Harmonic models are appropriate for time series with some periodicity built in, such as tidal data, temperature data, etc.

Suggested Citation

  • Dominique Haughton & Jonathan Haughton & Alan Izenman, 1994. "Model Selection in Harmonic Non-Linear Regression," Springer Books, in: H. Bozdogan & S. L. Sclove & A. K. Gupta & D. Haughton & G. Kitagawa & T. Ozaki & K. Tanabe (ed.), Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach, chapter 11, pages 187-207, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0866-9_12
    DOI: 10.1007/978-94-011-0866-9_12
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