Harmonic analysis of stationary time series
Marianna Bolla, Tamás Szabados · 2021
In this chapter, the authors concentrate on stationary time series, mainly in the wide sense, the behavior of which is irrespective of time shift. They prove equivalent notions of weak stationarity in terms of autocovariance matrix functions and matrix valued spectral measures. Spectral representation of the process itself is also given by orthogonal increments. There are some standard constructions of a stationary time series with a given covariance function or with a given spectral measure. It is important in practice if one can estimate parameters of a stationary time series by observing a single trajectory of the process for a long enough time.