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The ARMA model in state space form

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  • de Jong, Piet
  • Penzer, Jeremy

Abstract

This article explores alternative state space representations for ARMA models. We advocate representations that have minimal state order and appealing Kalman filter steady state properties. We derive expressions for smoother output and describe concrete connections to classical infinite sample representations.

Suggested Citation

  • de Jong, Piet & Penzer, Jeremy, 2004. "The ARMA model in state space form," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 119-125, October.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:119-125
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    1. Díaz, Guzmán & Moreno, Blanca & Coto, José & Gómez-Aleixandre, Javier, 2015. "Valuation of wind power distributed generation by using Longstaff–Schwartz option pricing method," Applied Energy, Elsevier, vol. 145(C), pages 223-233.
    2. Enrique Martínez García, 2020. "A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form," Globalization Institute Working Papers 389, Federal Reserve Bank of Dallas.
    3. Anderson, Brian D.O. & Deistler, Manfred & Felsenstein, Elisabeth & Koelbl, Lukas, 2016. "The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case," Journal of Econometrics, Elsevier, vol. 192(2), pages 366-373.
    4. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362, Edward Elgar Publishing.
    5. 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.
    6. Bórawski, Piotr & Bełdycka-Bórawska, Aneta & Jankowski, Krzysztof Jóżef & Dubis, Bogdan & Dunn, James W., 2020. "Development of wind energy market in the European Union," Renewable Energy, Elsevier, vol. 161(C), pages 691-700.
    7. Hang Qian, 2014. "A Flexible State Space Model And Its Applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 79-88, March.
    8. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    9. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    10. Piotr Bórawski & Marta Guth & Aneta Bełdycka-Bórawska & Krzysztof Józef Jankowski & Andrzej Parzonko & James W. Dunn, 2020. "Investments in Polish Agriculture: How Production Factors Shape Conditions for Environmental Protection?," Sustainability, MDPI, vol. 12(19), pages 1-26, October.
    11. Tommaso Proietti, 2021. "Predictability, real time estimation, and the formulation of unobserved components models," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 433-454, April.
    12. Chuanjie Xie & Chong Huang & Deqiang Zhang & Wei He, 2021. "BiLSTM-I: A Deep Learning-Based Long Interval Gap-Filling Method for Meteorological Observation Data," IJERPH, MDPI, vol. 18(19), pages 1-12, September.
    13. Piotr Bórawski & Marek Bartłomiej Bórawski & Andrzej Parzonko & Ludwik Wicki & Tomasz Rokicki & Aleksandra Perkowska & James William Dunn, 2021. "Development of Organic Milk Production in Poland on the Background of the EU," Agriculture, MDPI, vol. 11(4), pages 1-25, April.

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