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Long-Run Forecasting in Multicointegrated Systems


  • Siliverstovs, Boriss

    () (DIW Berlin)

  • Engsted, Tom

    () (Department of Finance, Aarhus School of Business)

  • Haldrup, Niels

    () (University of Aarhus)


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 evaluation 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.

Suggested Citation

  • Siliverstovs, Boriss & Engsted, Tom & Haldrup, Niels, 2002. "Long-Run Forecasting in Multicointegrated Systems," Finance Working Papers 02-14, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  • Handle: RePEc:hhb:aarfin:2002_014

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    References listed on IDEAS

    1. 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 237-254, May.
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    Cited by:

    1. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
    2. Athanasopoulos, George & Issler, João Victor & Guillen, Osmani Teixeira Carvalho, 2005. "Forecasting accuracy and estimation uncertainty using VAR models with short- and long-term economic restrictions: a Monte-Carlo study," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 589, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    3. Neri, Marcelo Cortes & Soares, Wagner Lopes, 2008. "Turismo sustentável e alivio a pobreza: avaliação de impacto," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 689, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    4. Holler, Manfred & Skott, Peter, "undated". "The importance of setting the agenda," Economics Working Papers 2003-8, Department of Economics and Business Economics, Aarhus University.
    5. Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
    6. Haldrup, Niels, "undated". "Empirical analysis of price data in the delineation of the relevant geographical market in competition analysis," Economics Working Papers 2003-9, Department of Economics and Business Economics, Aarhus University.
    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.

    More about this item


    Common Features; Multicointegration; Forecasting; VAR models;

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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