Hyper-spherical and elliptical stochastic cycles
AbstractA 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. Copyright Copyright 2010 Blackwell Publishing Ltd
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Journal of Time Series Analysis.
Volume (Year): 31 (2010)
Issue (Month): 3 (05)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
Other versions of this item:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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- James Morley & Charles Nelson & Eric Zivot, 2002.
"Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?,"
UWEC-2002-01, University of Washington, Department of Economics.
- James Morley & Charles Nelson & Eric Zivot, 2003. "Why are Beveridge-Nelson and Unobserved-component decompositions of GDP so Different?," Working Papers UWEC-2002-18-P, University of Washington, Department of Economics.
- James C. Morley & Charles Nelson & Eric Zivot, 2000. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Discussion Papers in Economics at the University of Washington 0013, Department of Economics at the University of Washington.
- James C. Morley & Charles Nelson & Eric Zivot, 2000. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Working Papers 0013, University of Washington, Department of Economics.
- Charles Nelson & Eric Zivot, 2000. "Why are Beveridge-Nelson and Unobserved-Component Decompositions of GDP so Different?," Econometric Society World Congress 2000 Contributed Papers 0692, Econometric Society.
- Harvey, A.C. & Trimbur, T.M., 2001.
"General Model-based Filters for Extracting Cycles and Trends in Economic Time Series,"
Cambridge Working Papers in Economics
0113, Faculty of Economics, University of Cambridge.
- Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
- Wenyang Zhang & Qiwei Yao & Howell Tong & Nils Chr Stenseth, 2003. "Smoothing for spatiotemporal models and its application to modeling Muskrat-Mink interaction," LSE Research Online Documents on Economics 5832, London School of Economics and Political Science, LSE Library.
- Zellner, Arnold & Palm, Franz, 1974.
"Time series analysis and simultaneous equation econometric models,"
Journal of Econometrics,
Elsevier, vol. 2(1), pages 17-54, May.
- ZELLNER, Arnold & PALM, Franz, . "Time series analysis and simultaneous equation econometric models," CORE Discussion Papers RP -173, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543, September.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- James C. Morley & Charles R. Nelson & Eric Zivot, 2003.
"Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?,"
The Review of Economics and Statistics,
MIT Press, vol. 85(2), pages 235-243, May.
- Tom Doan, . "RATS programs to replicate Morley-Nelson-Zivot state space decomposition," Statistical Software Components RTZ00115, Boston College Department of Economics.
- Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
- Proietti, Tommaso & Luati, Alessandra, 2013.
"The Exponential Model for the Spectrum of a Time Series: Extensions and Applications,"
45280, University Library of Munich, Germany.
- Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CEIS Research Paper 272, Tor Vergata University, CEIS, revised 19 Apr 2013.
- Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CREATES Research Papers 2013-34, School of Economics and Management, University of Aarhus.
- Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
- Alessandra Luati & Tommaso Proietti & Marco Reale, 2012.
"The Variance Profile,"
Journal of the American Statistical Association,
Taylor & Francis Journals, vol. 107(498), pages 607-621, June.
- Tommaso Proietti & Alessandra Luati, 2013. "Generalised Linear Spectral Models," CEIS Research Paper 290, Tor Vergata University, CEIS, revised 03 Oct 2013.
- Tommaso, Proietti & Alessandra, Luati, 2012.
"Maximum likelihood estimation of time series models: the Kalman filter and beyond,"
39600, University Library of Munich, Germany.
- Luati, Alessandra & Proietti, Tommaso, 2012. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Working Papers 02 BAWP, University of Sydney Business School, Discipline of Business Analytics.
- Giacomo Sbrana & Andrea Silvestrini, 2012. "Temporal aggregation of cyclical models with business cycle applications," Statistical Methods and Applications, Springer, vol. 21(1), pages 93-107, March.
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