Harmonic time-series and least squares

Abstract

It is assumed that a harmonic time-series model is the sum of a periodic sure function with (only) unknown linear parameters and of a random part, whose values are independent and identically distributed, with known distribution, linearly transformed. The Markoff justification of the least-squares method is used to obtain linear estimators of the linear parameters and the quadratic estimator of the scale parameter. The asymptotic distributions of the estimators are given and, based on them, some tests for the significance of the periods are obtained. A prediction formula is given also. An example is given.