## Abstract

Abstract. The problem is that of determining the parameters in a trigonometric polynomial when it is observed with added stationary noise. The frequencies, in particular, must be determined and the situation especially considered is that where these are close together. A similar problem arises if an angular frequency is close to zero or π. The method of estimation is the maximization of the regression sum of squares as a function of the unknown frequencies. In the asymptotic theory, the closely adjacent frequencies are separated by an amount that is of the order T^{‐1}, where T is the length of the series. Simulations show that this asymptotic treatment gives a better approximation in cases where the separation is of this magnitude than that obtained by treating the frequencies as fixed.

Original language | English |
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Pages (from-to) | 13-31 |

Number of pages | 19 |

Journal | Journal of Time Series Analysis |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 |

Externally published | Yes |

## Keywords

- frequency estimation
- maximum entropy
- regularity
- spectral line
- Trigonometric regression
- weak mixing