Kbiri, Mohammed Alaoui and Ghassan, Hassan Belkacem (2019): Model reduction in dynamical VAR systems. Published in: International Journal of Applied Mathematics and Statistics , Vol. 59, No. 3 (2020): pp. 12-20.
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Abstract
In this paper, we propose an alternative method that applies the model reduction techniques to the VAR framework when the number of variables is sufficiently large. The relevance of the model reduction in the VAR and SVAR systems comes from that the new trajectories preserve the qualitative properties of the initial trajectories. In economic analysis, this allows us to apprehend the underlying phenomena. Also, the resulting model is accurate, computationally less expensive, and based on the real meaning of the system.
Item Type: | MPRA Paper |
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Original Title: | Model reduction in dynamical VAR systems |
Language: | English |
Keywords: | Complexity; Dynamic system; Dimension reduction; Economic analysis; Reduced VAR; Reduced structural VAR. |
Subjects: | C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C55 - Large Data Sets: Modeling and Analysis |
Item ID: | 122971 |
Depositing User: | Professor Hassan Ghassan |
Date Deposited: | 17 Dec 2024 07:55 |
Last Modified: | 17 Dec 2024 07:55 |
References: | Adragni KP., Cook RD. (2009). Sufficient dimension reduction and prediction in regression. Philosophical Transactions of the Royal Society A 367: 4385-4405. Anjos, MF, Higham, NJ, Takouda, PL and Wolkowicz, H (2003). A Semidefinite Programming Approach for the Nearest Correlation Matrix Problem, Preliminary Research Report, Dept. Combinatorics & Optimization, Waterloo, Ontario. Antoulas AC. (2005). Approximation of Large-Scale Dynamical Systems, SIAM. ISBN: 978-0-898716-58-0. Antoulas AC. (1998). Approximation of linear operators in the 2-norm. Special Issue of LAA (Linear Algebra and Applications) on Challenges in Matrix Theory, 278: 309-316. Antoulas AC. (1999). Approximation of linear dynamical systems. In the Wiley Encyclopedia of Electrical and Electronics Engineering, edited by J.G. Webster, volume 11: 403-422. Amisano G., Giannini C. (1997). Topics in Structural VAR Econometrics. 2d Edition, Springer-Verlag, Berlin. Bartels, R. H.; Stewart, G. W. (1972). Solution of the matrix equation AX+XB=C. Comm. ACM. 15 (9): 820–826. doi:10.1145/361573.361582. Bernanke B., Boivin J., Eliasz PS. (2005). Measuring the effects of monetary policy: a factor-augmented vector autoregressive (FAVAR) approach. Q. J. Econ. 120(1): 387–422. Blanchard OJ., Quah D. (1989). The Dynamic Effect of Aggregate Demand and Supply Disturbances. American Economic Review 79(4): 655-673. Bhatia R., Rosenthal P. (1997). How and why to solve the operator equation AX-XB=Y? Bull. London Math. Soc. 29 (1): 1–21. doi:10.1112/S0024609396001828. Cook RD. (2007). Fisher Lecture: Dimension Reduction in Regression. Statistical Science 22(1): 1–26. Enns DF. (1984). Model reduction with balanced realizations: an error bound and frequency weighted generalizations. In Proc. of 23rd Conf. on Decision and Control, pages 127-132, Las Vegas, NV. Ghassan HB., Souissi M., Kbiri Alaoui M. (2009). An Alternative Identification of the Economic Shocks in SVAR Models. Economics Bulletin 29(2): 1028-1035. Grimme EJ. (1997). Krylov Projections Methods for Model Reduction, Ph.D. Thesis, ECE Dept., U., Illinois, Urbana-Champaign. Grimme EJ., Sorensen DC., Van Dooren P. (1995). Model reduction of state space systems via an implicitly restarted Lanczos method. Numerical Algorithms 12: 1-31. Higham, NJ. (2002). Computing the nearest correlation matrix- a problem from finance. IMA Journal of Numerical Analysis 22: 329-343. Higham NJ. (2000). QR factorization with complete pivoting and accurate computation of the SVD. Linear Algebra and its Applications 309: 153-174. King RG., Plosser CI., Stock JH., Watson MW. (1991). Stochastic Trends and Economics Fluctuations. American Economic Review 81: 819-840. Moore BC. (1981). Principal component analysis in linear systems: Controllability, Observability, and model reduction. IEEE Trans. Automat. Control 26(1): 17-32. Pernebo L., Silverman LM. (1982). Model reduction via balanced truncation state representation. IEEE Trans. Automat. Control 27(2): 382-387. Safonov MG., Chiang RY. (1989). A Schur method for balanced truncation model reduction. IEEE Trans. Automat. Control 34(7): 729-733. Shapiro MD., Watson MW. (1988). Sources of Business Cycle Fluctuations. NBER Working Paper number 2589. Stock JH, Watson MW. (2001). Vector autoregressions. Journal of Economic Perspectives 15(4): 101–115. Stock JH., Watson MW. (2006). Forecasting with many predictors. In Handbook of Economic Forecasting, Vol. 1, ed. G Elliott, C Granger, A Timmermann, pages 515–554. Amsterdam: North-Holland. Sims C. (1980). Macroeconomics and Reality. Econometrica 48(1): 153-174. Snowden ThJ., Van Der Graaf PH., Tindall MJ. (2017). Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends. Bulletin of Mathematical Biology 79: 1449–1486. Tombs MS., Postlethwaite I. (1987). Truncated balanced realization of a stable non-minimal state-space system. International Journal of Control 46(4): 1319-1330. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/122971 |