ABSTRACT
Spectral analysis is concerned with estimating the spectrum over the whole range of frequencies. This chapter is mainly concerned with purely indeterministic processes, which have a continuous spectrum, but the techniques can be used for deterministic processes to pick out periodic components in the presence of noise. Traditional spectral analysis is essentially a modification of Fourier analysis so as to make it suitable for stochastic rather than deterministic functions of time. Fourier analysis is essentially concerned with approximating a function by a sum of sine and cosine terms, called the Fourier series representation. The chapter describes several alternative ways of estimating a spectrum. Each method provides a consistent estimator for the spectral density function, in contrast to the periodogram. For a non-stationary series, the estimated spectrum of the detrended, deseasonalized data will depend to some extent on the method chosen to remove trend and seasonality.
