Spectra of Stationary Processes

Uwe Hassler

Chapter 4 in Stochastic Processes and Calculus, 2016, pp 77-101 from Springer

Abstract: Abstract Spectral analysis (or analysis in the frequency domain) aims at detecting cyclical movements in a time series. These may originate from seasonality, a trend component or from a business cycle. The theoretical spectrum of a stationary process is the quantity measuring how strongly cycles with a certain period, or frequency, account for total variance. Typically, elaborations on spectral analysis are formally demanding requiring e.g. knowledge of complex numbers and Fourier transformations. In this textbook we have tried for a way of presenting and deriving the relevant results being less elegant but in return managing with less mathematical burden. The next section provides the definitions and intuition behind spectral analysis. Section 4.3 is analytically more demanding containing some general theory. This theory is exemplified with the discussion of spectra from particular ARMA processes, hence building on the previous chapter.

Keywords: Business Cycle; Spectral Density Function; Previous Chapter; Trend Component; Frequency Zero (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-23428-1_4

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