Preface

Summary

In late 1982, Ted Hannan discussed with me a question he had been asked by some astronomers – how could you estimate the two frequencies in two sinusoids when the frequencies were so close together that you could not tell, by looking at the periodogram, that there were two frequencies? He asked me if I would like to work with him on the problem and gave me a reprint of his paper (Hannan 1973) on the estimation of frequency. Together we wrote a paper (Hannan and Quinn 1989) which derived the regression sum of squares estimators of the frequencies, and showed that the estimators were strongly consistent and satisfied a central limit theorem. It was clear that there were no problems asymptotically if the two frequencies were fixed, so Ted's idea was to fix one frequency, and let the other converge to it at a certain rate, in much the same way as the alternative hypothesis is constructed to calculate the asymptotic power of a test. Since then, I have devoted much of my research to sinusoidal models. In particular, I have spent a lot of time constructing algorithms for the estimation of parameters in these models, to implementing the algorithms in practice and, for me perhaps the most challenging, establishing the asymptotic (large sample) properties of the estimators.