 Hyper‐spherical and elliptical stochastic cyclesAlessandra Luati and Tommaso Proietti Journal of Time Series Analysis, 2010, vol. 31, issue 3, 169-181 Abstract: A univariate first‐order stochastic cycle can be represented as an element of a bivariate first‐order vector autoregressive process, or VAR(1), where the transition matrix is associated with a rotation along a circle in the plane, and the reduced form is ARMA(2,1). This paper generalizes this representation in two directions. According to the first, the cyclical dynamics originate from the motion of a point along an ellipse. The reduced form is also ARMA(2,1), but the model can account for certain types of asymmetries. The second deals with the multivariate case: the cyclical dynamics result from the projection along one of the coordinate axis of a point moving in along an hyper‐sphere. This is described by a VAR(1) process whose transition matrix is obtained by a sequence of n‐dimensional Givens rotations. The reduced form of an element of the system is shown to be ARMA(n, n − 1). The properties of the resulting models are analysed in the frequency domain, and we show that this generalization can account for a multimodal spectral density. The illustrations show that the proposed generalizations can be fitted successfully to some well‐known case studies of the time series literature. Date: 2010 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:31:y:2010:i:3:p:169-181 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Time Series Analysis is currently edited by M.B. Priestley More articles in Journal of Time Series Analysis from Wiley Blackwell |
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