In many important textbooks the formal statement of the Spectral RepresentationTheorem is followed by a process version, usually informal, stating thatany stationary stochastic process g is the limit in quadratic mean of asequence of processes, each consisting of a finite sum of...

(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant...

This paper uses a frequency domain approach to gain insight into the correlation between survey indicators and year-on-year GDP growth. Using the Baxter-King filter, we split up each series into three components: a short-term, a business cycle (oscillations between 18 and 96 months) and a...