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Generation Of Time Series Models With Given Spectral Properties

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  • Georgi N. Boshnakov
  • Bisher M. Iqelan

Abstract

. We give a method for generation of periodically correlated and multivariate ARIMA models whose dynamic characteristics are partially or fully specified in terms of spectral poles and zeroes or their equivalents in the form of eigenvalues/eigenvectors of associated model matrices. Our method is based on the spectral decomposition of multi‐companion matrices and their factorization into products of companion matrices. Generated models are needed in simulation but may also be used in estimation, e.g. to set sensible initial values of parameters for nonlinear optimization. We are not aware of any other general method for multivariate linear systems of comparable generality and control over the spectral properties of the generated model.

Suggested Citation

  • Georgi N. Boshnakov & Bisher M. Iqelan, 2009. "Generation Of Time Series Models With Given Spectral Properties," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 349-368, May.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:3:p:349-368
    DOI: 10.1111/j.1467-9892.2009.00617.x
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    References listed on IDEAS

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    1. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    2. Paul Gilbert, 2000. "A note on the computation of time series model roots," Applied Economics Letters, Taylor & Francis Journals, vol. 7(7), pages 423-424.
    3. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
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    Cited by:

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    3. Constantin Anghelache & Madalina-Gabriela Anghel & Stefan Virgil Iacob, 2022. "Theoretical Aspects Regarding The Models Of The Financial - Monetary Analysis," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 1, pages 52-58, February.
    4. Leo Krippner, 2023. "Estimating and Applying Autoregression Models via Their Eigensystem Representation," CAMA Working Papers 2023-47, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    5. Radu Titus MARINESCU & Aurelian DIACONU & Alexandru BADIU & Alexandru BADIU, 2016. "Analyzing the correlation between GDP and import using a statistical-econometric model," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(10), pages 98-102, October.
    6. Bergmeir, Christoph & Costantini, Mauro & Benítez, José M., 2014. "On the usefulness of cross-validation for directional forecast evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 132-143.
    7. Madalina-Gabriela ANGHEL & Luminita Madalina CALOTA, 2016. "Statistical-econometric model used in performance analysis of the company," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(10), pages 33-40, October.
    8. Ramona-Maria DIMITROV, 2023. "Forecasts On Some Financial Indicators: A Case Study For S.C.D.A Simnic," Management and Marketing Journal, University of Craiova, Faculty of Economics and Business Administration, vol. 0(2), pages 185-211, November.

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