IDEAS home Printed from https://ideas.repec.org/p/rtv/ceisrp/556.html
   My bibliography  Save this paper

The Vector Error Correction Index Model: Representation, Estimation and Identification

Author

Abstract

This paper extends the multivariate index autoregressive model by Reinsel (1983) to the case of cointegrated time series of order (1, 1). In this new modelling, namely the Vector Error-Correction Index Model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction w.r.t. the Vector Error Correction Model. We show that the VECIM allows one to decompose the reduced form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US.

Suggested Citation

  • Gianluca Cubadda & Marco Mazzali, 2023. "The Vector Error Correction Index Model: Representation, Estimation and Identification," CEIS Research Paper 556, Tor Vergata University, CEIS, revised 04 Apr 2023.
  • Handle: RePEc:rtv:ceisrp:556
    as

    Download full text from publisher

    File URL: https://ceistorvergata.it/RePEc/rpaper/RP556.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.
    2. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    3. Paul Beaudry & Franck Portier, 2014. "News-Driven Business Cycles: Insights and Challenges," Journal of Economic Literature, American Economic Association, vol. 52(4), pages 993-1074, December.
    4. Chiara Casoli & Riccardo (Jack) Lucchetti, 2022. "Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices [Commodity-price comovement and global economic activity]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 494-514.
    5. Bernardini, Emmanuela & Cubadda, Gianluca, 2015. "Macroeconomic forecasting and structural analysis through regularized reduced-rank regression," International Journal of Forecasting, Elsevier, vol. 31(3), pages 682-691.
    6. Gregory C. Reinsel & Sung K. Ahn, 1992. "Vector Autoregressive Models With Unit Roots And Reduced Rank Structure:Estimation. Likelihood Ratio Test, And Forecasting," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 353-375, July.
    7. Matteo Barigozzi & Lorenzo Trapani, 2022. "Testing for Common Trends in Nonstationary Large Datasets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1107-1122, June.
    8. George-Marios Angeletos & Fabrice Collard & Harris Dellas, 2020. "Business-Cycle Anatomy," American Economic Review, American Economic Association, vol. 110(10), pages 3030-3070, October.
    9. Gary M. Koop, 2013. "Forecasting with Medium and Large Bayesian VARS," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 177-203, March.
    10. Cavaliere, Giuseppe & De Angelis, Luca & Rahbek, Anders & Robert Taylor, A.M., 2018. "Determining The Cointegration Rank In Heteroskedastic Var Models Of Unknown Order," Econometric Theory, Cambridge University Press, vol. 34(2), pages 349-382, April.
    11. Dieppe, Alistair & Francis, Neville & Kindberg-Hanlon, Gene, 2021. "The identification of dominant macroeconomic drivers: coping with confounding shocks," Working Paper Series 2534, European Central Bank.
    12. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3645-3657, March.
    13. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    14. Forni, Mario & Gambetti, Luca & Lippi, Marco & Sala, Luca, 2020. "Common Component Structural VARs," CEPR Discussion Papers 15529, C.E.P.R. Discussion Papers.
    15. Alexei Onatski & Chen Wang, 2018. "Alternative Asymptotics for Cointegration Tests in Large VARs," Econometrica, Econometric Society, vol. 86(4), pages 1465-1478, July.
    16. repec:ulb:ulbeco:2013/13388 is not listed on IDEAS
    17. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    18. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    19. Zhang, Rongmao & Robinson, Peter & Yao, Qiwei, 2019. "Identifying cointegration by eigenanalysis," LSE Research Online Documents on Economics 87431, London School of Economics and Political Science, LSE Library.
    20. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    21. Kasa, Kenneth, 1992. "Common stochastic trends in international stock markets," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 95-124, February.
    22. Giuseppe Cavaliere & Luca De Angelis & Anders Rahbek & A. M. Robert Taylor, 2015. "A Comparison of Sequential and Information-based Methods for Determining the Co-integration Rank in Heteroskedastic VAR Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 106-128, February.
    23. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    24. Harald Uhlig, 2004. "What moves GNP?," Econometric Society 2004 North American Winter Meetings 636, Econometric Society.
    25. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
    26. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2016. "Structural analysis with Multivariate Autoregressive Index models," Journal of Econometrics, Elsevier, vol. 192(2), pages 332-348.
    27. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
    28. Andrea Carriero & George Kapetanios & Massimiliano Marcellino, 2011. "Forecasting large datasets with Bayesian reduced rank multivariate models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 735-761, August.
    29. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    30. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    31. Gianluca Cubadda & Alain Hecq, 2011. "Testing for common autocorrelation in data‐rich environments," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(3), pages 325-335, April.
    32. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    33. Barsky, Robert B. & Sims, Eric R., 2011. "News shocks and business cycles," Journal of Monetary Economics, Elsevier, vol. 58(3), pages 273-289.
    34. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    35. Mario Forni & Luca Gambetti & Luca Sala, 2019. "Structural VARs and noninvertible macroeconomic models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 221-246, March.
    36. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    37. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    38. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    39. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.
    40. Centoni, Marco & Cubadda, Gianluca, 2003. "Measuring the business cycle effects of permanent and transitory shocks in cointegrated time series," Economics Letters, Elsevier, vol. 80(1), pages 45-51, July.
    41. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    42. Barigozzi, Matteo & Lippi, Marco & Luciani, Matteo, 2021. "Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with I(1) cointegrated factors," Journal of Econometrics, Elsevier, vol. 221(2), pages 455-482.
    43. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    44. Engle, Robert F. & Issler, João Victor, 1993. "Common trends and common cycles in Latin America," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 47(2), April.
    45. Ho, Mun S & Sorensen, Bent E, 1996. "Finding Cointegration Rank in High Dimensional Systems Using the Johansen Test: An Illustration Using Data Based Monte Carlo Simulations," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 726-732, November.
    46. Rongmao Zhang & Peter Robinson & Qiwei Yao, 2019. "Identifying Cointegration by Eigenanalysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 916-927, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    2. G. Cubadda & S. Grassi & B. Guardabascio, 2022. "The Time-Varying Multivariate Autoregressive Index Model," Papers 2201.07069, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    2. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    3. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.
    4. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    5. Matteo Barigozzi & Matteo Luciani, 2017. "Common Factors, Trends, and Cycles in Large Datasets," Finance and Economics Discussion Series 2017-111, Board of Governors of the Federal Reserve System (U.S.).
    6. Barigozzi, Matteo & Lippi, Marco & Luciani, Matteo, 2021. "Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with I(1) cointegrated factors," Journal of Econometrics, Elsevier, vol. 221(2), pages 455-482.
    7. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2022. "The global component of inflation volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 700-721, June.
    8. G. Cubadda & S. Grassi & B. Guardabascio, 2022. "The Time-Varying Multivariate Autoregressive Index Model," Papers 2201.07069, arXiv.org.
    9. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    10. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    11. Rangan Gupta & Alain Kabundi & Stephen Miller & Josine Uwilingiye, 2014. "Using large data sets to forecast sectoral employment," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 229-264, June.
    12. Chiara Casoli & Riccardo (Jack) Lucchetti, 2022. "Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices [Commodity-price comovement and global economic activity]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 494-514.
    13. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2016. "Non-Stationary Dynamic Factor Models for Large Datasets," Finance and Economics Discussion Series 2016-024, Board of Governors of the Federal Reserve System (U.S.).
    14. Cimadomo, Jacopo & Giannone, Domenico & Lenza, Michele & Monti, Francesca & Sokol, Andrej, 2022. "Nowcasting with large Bayesian vector autoregressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 500-519.
    15. Koop, Gary & Korobilis, Dimitris & Pettenuzzo, Davide, 2019. "Bayesian compressed vector autoregressions," Journal of Econometrics, Elsevier, vol. 210(1), pages 135-154.
    16. Francisco Corona & Pilar Poncela & Esther Ruiz, 2020. "Estimating Non-stationary Common Factors: Implications for Risk Sharing," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 37-60, January.
    17. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2016. "Structural analysis with Multivariate Autoregressive Index models," Journal of Econometrics, Elsevier, vol. 192(2), pages 332-348.
    18. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2020. "The economic drivers of volatility and uncertainty," Temi di discussione (Economic working papers) 1285, Bank of Italy, Economic Research and International Relations Area.
    19. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
    20. Gianluca Cubadda & Alain Hecq & Elisa Voisin, 2023. "Detecting Common Bubbles in Multivariate Mixed Causal–Noncausal Models," Econometrics, MDPI, vol. 11(1), pages 1-16, March.

    More about this item

    Keywords

    Vector autoregressive models; multivariate autoregressive index model; cointegration; reduced-rank regression; dimension reduction; main business cycle shock.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rtv:ceisrp:556. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Barbara Piazzi (email available below). General contact details of provider: https://edirc.repec.org/data/csrotit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.