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Properties of higher order stochastic cycles
Author(s) -
Trimbur Thomas M.
Publication year - 2006
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.0143-9782.2005.00462.x
Subject(s) - mathematics , econometrics , series (stratigraphy) , multivariate statistics , interpretation (philosophy) , stochastic modelling , class (philosophy) , bayesian probability , variety (cybernetics) , frequency domain , stochastic process , statistics , computer science , artificial intelligence , mathematical analysis , paleontology , biology , programming language
. This article investigates a general class of stochastic cycles, presenting the main properties in the time and frequency domains. Harvey and Trimbur [Review of Economics and statistics (2003) Vol. 85, pp. 244–55] showed how generalized cyclical processes may be used in unobserved components models to extract smoother cycles in economic series. The stochastic cycle models allow for a flexible description of periodic behaviour in time series data. In the frequency domain, a wide variety of peaked spectral shapes, characteristic of time‐varying cyclical dynamics, is produced. The parameters have a direct interpretation, so cyclical behaviour may be studied directly; in a Bayesian approach, the researcher may implement prior views on the period in a consistent way. Extensions to multivariate models are possible.