This paper is concerned with the study of time series models which are linear combinations of normal variables with zero means and variances σ2t(t= 0, ±1, ±2, …). Ifxt(t= 1, 2, …,N) is a realization of a time series, the periodogram ofX2tis employed to discover the dominant frequencies in σ2t, where σ2tis expressed in a finite Fourier series. In Part I of the paper it is proved that this periodogram is, in some sense discussed in the paper, a consistent estimator of a product of the absolute value of the Fourier coefficients and a function of the linear model coefficients; then an approximate method for estimating the Fourier coefficients separately is given.