Determining the number of terms in a trigonometric regression. (English) Zbl 0814.62053
Summary: We consider the estimation of the number of sinusoidal terms in a time series contaminated by additive noise with unknown correlation structure. The method fits sinusoidal terms by least squares and models the noise component using a high order autoregression. A criterion based on the minimum description length principle is used to select the number of sinusoidal terms and the order of the noise model. The small sample efficacy of the model selection procedure is examined by simulations and the analysis of some astronomical data. Consistency is proved under quite general conditions on the noise spectrum.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
sinusoidal regression; structure selection; consistency; number of sinusoidal terms; time series; additive noise; unknown correlation; least squares; high order autoregression; minimum description length principle; small sample efficacy; model selection procedure; simulations; astronomical dataReferences:
| [1] | Baldwin A. J., S. Carinae. R. Astron. Soc. N. Z. (Variable Star Sect.) 6 pp 31– (1978) |
| [2] | Brillinger D. R., Applied Probability, Stochastic Processes and Sampling Theory pp 75– (1987) · doi:10.1007/978-94-009-4786-3_6 |
| [3] | Hannan E. J., Developments in Time Series Analysis pp 127– (1993) · doi:10.1007/978-1-4899-4515-0_10 |
| [4] | DOI: 10.1016/0304-4149(86)90117-1 · Zbl 0613.60024 · doi:10.1016/0304-4149(86)90117-1 |
| [5] | DOI: 10.1016/0047-259X(89)90055-9 · Zbl 0689.62078 · doi:10.1016/0047-259X(89)90055-9 |
| [6] | Quinn B. G., J. Time Ser. Anal. 10 pp 71– (1989) |
| [7] | DOI: 10.2307/2337018 · doi:10.2307/2337018 |
| [8] | Rissanen J., Stochastic Complexity in Scientific Enquiry. (1989) · Zbl 0800.68508 |
| [9] | Wang Xiaobao., J. Time Ser. Anal. 14 pp 431– (1993) |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
