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Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation

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  • Funovits, Bernd

Abstract

This article focuses on the parametrisation, identifiability, and (quasi-) maximum likelihood (QML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models. SVAR models are routinely adopted due to their well-known implementation strategy. However, for various economic and statistical reasons, multivariate SVARMA settings are often more suitable. These settings introduce complexity in the analysis, primarily due to the presence of the moving average (MA) polynomial. We propose a novel representation of the MA polynomial matrix using the Wiener–Hopf factorization (WHF). A significant advantage of the WHF is its ability to handle possible non-invertibility and thus models with informational asymmetry between economic agents and outside observers. Since solutions of Dynamic Stochastic General Equilibrium (DSGE) models often involve this informational asymmetry, SVARMA models in WHF parametrisation can be considered data-driven alternatives to DSGE models and used for their evaluation. Furthermore, we provide low-level conditions for the asymptotic normality of the (Q)ML estimator and analytic expressions for the score and information matrix. As application, we estimate the Blanchard and Quah model, and compare our results and implied impulse response function with the ones in the SVAR model by Blanchard and Quah and a non-invertible SVARMA model by Gouriéroux and co-authors. Importantly, we have implemented this novel method in a well-documented R-package, making it readily accessible for researchers and practitioners.

Suggested Citation

  • Funovits, Bernd, 2024. "Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation," Journal of Econometrics, Elsevier, vol. 241(2).
  • Handle: RePEc:eee:econom:v:241:y:2024:i:2:s030440762400112x
    DOI: 10.1016/j.jeconom.2024.105766
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    as
    1. Poskitt, D.S., 2016. "Vector autoregressive moving average identification for macroeconomic modeling: A new methodology," Journal of Econometrics, Elsevier, vol. 192(2), pages 468-484.
    2. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    3. Mala Raghavan & George Athanasopoulos & Param Silvapulle, 2016. "Canadian monetary policy analysis using a structural VARMA model," Canadian Journal of Economics, Canadian Economics Association, vol. 49(1), pages 347-373, February.
    4. Bernd Funovits, 2020. "Comment on Gouri\'eroux, Monfort, Renne (2019): Identification and Estimation in Non-Fundamental Structural VARMA Models," Papers 2010.02711, arXiv.org.
    5. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    6. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    7. Deistler, Manfred & Seifert, Hans-Gunther, 1978. "Identifiability and Consistent Estimability in Econometric Models," Econometrica, Econometric Society, vol. 46(4), pages 969-980, July.
    8. Lippi, Marco & Reichlin, Lucrezia, 1994. "VAR analysis, nonfundamental representations, blaschke matrices," Journal of Econometrics, Elsevier, vol. 63(1), pages 307-325, July.
    9. Ravenna, Federico, 2007. "Vector autoregressions and reduced form representations of DSGE models," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2048-2064, October.
    10. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    11. Marc Hallin & Chintan Mehta, 2015. "R -Estimation for Asymmetric Independent Component Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 218-232, March.
    12. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    13. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    14. Nikolay Gospodinov & Serena Ng, 2015. "Minimum Distance Estimation of Possibly Noninvertible Moving Average Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 403-417, July.
    15. Yao, Wenying & Kam, Timothy & Vahid, Farshid, 2017. "On weak identification in structural VARMA models," Economics Letters, Elsevier, vol. 156(C), pages 1-6.
    16. Blanchard, Olivier Jean & Quah, Danny, 1993. "The Dynamic Effects of Aggregate Demand and Supply Disturbances: Reply," American Economic Review, American Economic Association, vol. 83(3), pages 653-658, June.
    17. Christian Gouriéroux & Jean-Michel Zakoïan, 2017. "Local explosion modelling by non-causal process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 737-756, June.
    18. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    19. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    20. Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, vol. 47(4), pages 1005-1030, July.
    21. George Athanasopoulos & Farshid Vahid, 2008. "A complete VARMA modelling methodology based on scalar components," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 533-554, May.
    22. Bin Chen & Jinho Choi & Juan Carlos Escanciano, 2017. "Testing for fundamental vector moving average representations," Quantitative Economics, Econometric Society, vol. 8(1), pages 149-180, March.
    23. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    24. M. Deistler, 1975. "z-Transform and identification of linear econometric models with autocorrelated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 13-25, December.
    25. Hannan, E J, 1971. "The Identification Problem for Multiple Equation Systems with Moving Average Errors," Econometrica, Econometric Society, vol. 39(5), pages 751-765, September.
    26. Lippi, Marco & Reichlin, Lucrezia, 1993. "The Dynamic Effects of Aggregate Demand and Supply Disturbances: Comment," American Economic Review, American Economic Association, vol. 83(3), pages 644-652, June.
    27. Sargent, Thomas J., 1979. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Journal of Monetary Economics, Elsevier, vol. 5(1), pages 133-143, January.
    28. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, September.
    29. Athanasopoulos, George & Vahid, Farshid, 2008. "VARMA versus VAR for Macroeconomic Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 237-252, April.
    30. Deistler, Manfred, 1983. "The Properties of the Parameterization of ARMAX Systems and Their Relevance for Structural Estimation and Dynamic Specification," Econometrica, Econometric Society, vol. 51(4), pages 1187-1207, July.
    31. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, September.
    32. Kung-Sik Chan & Lop-Hing Ho & Howell Tong, 2006. "A note on time-reversibility of multivariate linear processes," Biometrika, Biometrika Trust, vol. 93(1), pages 221-227, March.
    33. D. S. Poskitt & Wenying Yao, 2017. "Vector Autoregressions and Macroeconomic Modeling: An Error Taxonomy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 407-419, July.
    34. Sirkku Pauliina Ilmonen & Davy Paindaveine, 2011. "Semiparametrically Efficient Inference Based on Signed Ranks in Symmetric Independent Component Models," Working Papers ECARES ECARES 2011-003, ULB -- Universite Libre de Bruxelles.
    35. Lii, Keh-Shin & Rosenblatt, Murray, 1992. "An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 272-299, November.
    36. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February.
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    More about this item

    Keywords

    Non-invertibility; Wiener–Hopf factorisation; Structural Vector Autoregressive Moving-Average Models; Non-Gaussianity; Identifiability;
    All these keywords.

    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
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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