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Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form

Author

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  • George Athanasopoulos
  • D. Poskitt
  • Farshid Vahid

Abstract

In this article we study two methodologies which identify and specify canonical form VARMA models. The two methodologies are: (1) an extension of the scalar component methodology which specifies canonical VARMA models by identifying scalar components through canonical correlations analysis; and (2) the Echelon form methodology, which specifies canonical VARMA models through the estimation of Kronecker indices. We compare the actual forms and the methodologies on three levels. Firstly, we present a theoretical comparison. Secondly, we present a Monte Carlo simulation study that compares the performances of the two methodologies in identifying some pre-specified data generating processes. Lastly, we compare the out-of-sample forecast performance of the two forms when models are fitted to real macroeconomic data.

Suggested Citation

  • George Athanasopoulos & D. Poskitt & Farshid Vahid, 2012. "Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 60-83.
    • Handle: RePEc:taf:emetrv:v:31:y:2012:i:1:p:60-83
    DOI: 10.1080/07474938.2011.607088
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    Cited by:

    1. D.S. Poskitt, 2009. "Vector Autoregresive Moving Average Identification for Macroeconomic Modeling: Algorithms and Theory," Monash Econometrics and Business Statistics Working Papers 12/09, Monash University, Department of Econometrics and Business Statistics.
    2. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    3. Gil-Alana, Luis A. & Gupta, Rangan & Olubusoye, Olusanya E. & Yaya, OlaOluwa S., 2016. "Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, Elsevier, vol. 109(C), pages 29-37.
    4. Mendoza, Daniel E. & Ochoa-Sánchez, Ana & Samaniego, Esteban P., 2022. "Forecasting of a complex phenomenon using stochastic data-based techniques under non-conventional schemes: The SARS-CoV-2 virus spread case," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. George Athanasopoulos & Donald S. Poskitt & Farshid Vahid & Wenying Yao, 2016. "Determination of Long‐run and Short‐run Dynamics in EC‐VARMA Models via Canonical Correlations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 1100-1119, September.
    6. Siva R Venna & Satya Katragadda & Vijay Raghavan & Raju Gottumukkala, 2021. "River Stage Forecasting using Enhanced Partial Correlation Graph," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(12), pages 4111-4126, September.
    7. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    8. Joshua C.C. Chan & Eric Eisenstat, 2015. "Efficient estimation of Bayesian VARMAs with time-varying coefficients," CAMA Working Papers 2015-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    9. Abhimanyu Mukerji & Sushant More & Ashwin Viswanathan Kannan & Lakshmi Ravi & Hua Chen & Naman Kohli & Chris Khawand & Dinesh Mandalapu, 2024. "Valuing an Engagement Surface using a Large Scale Dynamic Causal Model," Papers 2408.11967, arXiv.org.
    10. Alfredo Garcia-Hiernaux & Jose Casals & Miguel Jerez, 2024. "Identification of canonical models for vectors of time series: a subspace approach," Statistical Papers, Springer, vol. 65(3), pages 1493-1530, May.
    11. Athanasopouolos, George & Poskitt, Don & Vahid, Farshid & Yao, Wenying, 2014. "Forecasting with EC-VARMA models," Working Papers 2014-07, University of Tasmania, Tasmanian School of Business and Economics, revised 22 Feb 2014.
    12. Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2016. "Large Bayesian VARMAs," Journal of Econometrics, Elsevier, vol. 192(2), pages 374-390.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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