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Long-Run Forecasting in Multicointegrated Systems

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  • Boriss Siliverstovs
  • Tom Engsted
  • Niels Haldrup

Abstract

In this paper long-run forecasting of multicointegrating variables is investigated. Multicointegration typically occurs in dynamic systems involving both stock and flow variables whereby a common feature in the form of shared stochastic trends is present across different levels of multiple time series. Hence, the effect of imposing this "common feature" restriction on out-of-sample valuation and forecasting accuracy of such variables is of interest. In particular, we compare the long-run forecasting performance of the multicointegrated variables between a model that correctly imposes the "common feature" restrictions and a (univariate) model that omits these multicointegrating restrictions completely. We employ different loss functions based on a range of mean square forecast error criteria, and the results indicate that different loss functions result in different ranking of models with respect to their infinite horizon forecasting performance. We consider loss functions using a standard trace mean square forecast error criterion (penalizing the forecast errors of flow variables only), and a loss function evaluating forecast errors of changes in both stock and flow variables. The latter loss function is based on the triangular representation of cointegrated systems and was initially suggested by Christoffersen and Diebold (1998). It penalizes deviations from long-run relations among the flow variables through cointegrating restrictions. We present a new loss function which further penalizes deviations in the long run relationship between the levels of stock and flow variables. It is derived from the triangular representation of multicointegrated systems. Using this criterion, system forecasts from a model incorporating multicointegration restrictions dominate forecasts from univariate models. The paper highlights the importance of carefully selecting loss functions in forecast evaluation of models involving stock and flow variables.

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Bibliographic Info

Paper provided by DIW Berlin, German Institute for Economic Research in its series Discussion Papers of DIW Berlin with number 381.

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Length: 28 p.
Date of creation: 2003
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Handle: RePEc:diw:diwwpp:dp381

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References

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  1. Clara Jørgensen & Hans Christian Kongsted & Anders Rahbek, 1996. "Trend-Stationarity in the I(2) Cointegration Model," Discussion Papers 96-12, University of Copenhagen. Department of Economics.
  2. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  3. Engsted, Tom & Haldrup, Niels, 1999. " Multicointegration in Stock-Flow Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(2), pages 237-54, May.
  4. Engsted, Tom & Gonzalo, Jesus & Haldrup, Niels, 1997. "Testing for multicointegration," Economics Letters, Elsevier, vol. 56(3), pages 259-266, November.
  5. Anindya Banerjee & Lynne Cockerell & Bill Russell, 2001. "An I(2) analysis of inflation and the markup," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 221-240.
  6. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S145-59, Supplemen.
  7. Boriss Siliverstovs, 2006. "Multicointegration in US consumption data," Applied Economics, Taylor & Francis Journals, vol. 38(7), pages 819-833.
  8. Peter F. Christoffersen & Francis X. Diebold, 1997. "Cointegration and Long-Horizon Forecasting," NBER Technical Working Papers 0217, National Bureau of Economic Research, Inc.
  9. Clements, M.P. & Hendry, D.F., 1992. "Forecasting in Cointegrated Systems," Economics Series Working Papers 99139, University of Oxford, Department of Economics.
  10. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
  11. John Y. Campbell & Robert J. Shiller, 1988. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  12. Clements, Michael P & Hendry, David F, 1995. "Forecasting in Cointegration Systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 127-46, April-Jun.
  13. Clements, M.P. & Hendry, D., 1992. "On the Limitations of Comparing Mean Square Forecast Errors," Economics Series Working Papers 99138, University of Oxford, Department of Economics.
  14. Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
  15. Niels Haldrup, 1998. "An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
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Citations

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Cited by:
  1. Athanasopoulos, George & Guillén, Osmani Teixeira de Carvalho & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Economics Working Papers (Ensaios Economicos da EPGE) 713, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  2. Nielsen, Morten Oe., . "Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence," Economics Working Papers 2002-16, School of Economics and Management, University of Aarhus.
  3. Osmani Teixeira de Carvalho Guillén & João Victor Issler & George Athanasopoulos, 2006. "Forecasting Accuracy and Estimation Uncertainty using VAR Models with Short- and Long-Term Economic Restrictions: A Monte-Carlo Study," IBMEC RJ Economics Discussion Papers 2006-01, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  4. Haldrup, Niels, . "Empirical analysis of price data in the delineation of the relevant geographical market in competition analysis," Economics Working Papers 2003-9, School of Economics and Management, University of Aarhus.
  5. Neri, Marcelo Cortes & Soares, Wagner Lopes, 2008. "Turismo sustentável e alivio a pobreza: avaliação de impacto," Economics Working Papers (Ensaios Economicos da EPGE) 689, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  6. Holler, Manfred & Skott, Peter, . "The importance of setting the agenda," Economics Working Papers 2003-8, School of Economics and Management, University of Aarhus.
  7. Heather M Anderson & Farshid Vahid, 2010. "VARs, Cointegration and Common Cycle Restrictions," Monash Econometrics and Business Statistics Working Papers 14/10, Monash University, Department of Econometrics and Business Statistics.

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