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Forecasting Levels of log Variables in Vector Autoregressions

Author

Listed:
  • Gunnar Bårdsen

    (Department of Economics, Norwegian University of Science and Technology)

  • Helmut Lütkepohl
Abstract
Sometimes forecasts of the original variable are of interest al- though a variable appears in logarithms (logs) in a system of time series. In that case converting the forecast for the log of the variable to a naive forecast of the original variable by simply applying the exponential transformation is not optimal theoretically. A simple expression for the optimal forecast un- der normality assumptions is derived. Despite its theoretical advantages the optimal forecast is shown to be inferior to the naive forecast if speci¯cation and estimation uncertainty are taken into account. Hence, in practice using the exponential of the log forecast is preferable to using the optimal forecast.

Suggested Citation

  • Gunnar Bårdsen & Helmut Lütkepohl, 2009. "Forecasting Levels of log Variables in Vector Autoregressions," Working Paper Series 10409, Department of Economics, Norwegian University of Science and Technology.
    • Handle: RePEc:nst:samfok:10409
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    File URL: http://www.svt.ntnu.no/iso/WP/2009/7_logVAR1.pdf
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    References listed on IDEAS

    as
    1. Arino, Miguel A. & Franses, Philip Hans, 2000. "Forecasting the levels of vector autoregressive log-transformed time series," International Journal of Forecasting, Elsevier, vol. 16(1), pages 111-116.
    2. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    3. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, vol. 42(3), pages 619-638, June.
    4. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    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.
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    Cited by:

    1. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    2. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España.
    3. Pascual, Lorenzo & Fresoli, Diego Eduardo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Matteo Luciani & David Veredas, "undated". "A simple model for vast panels of volatilities," ULB Institutional Repository 2013/136239, ULB -- Universite Libre de Bruxelles.
    5. Mayr, Johannes & Ulbricht, Dirk, 2015. "Log versus level in VAR forecasting: 42 million empirical answers—Expect the unexpected," Economics Letters, Elsevier, vol. 126(C), pages 40-42.
    6. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    7. Lo, Danny K. & Hall, Anthony D., 2015. "Resiliency of the limit order book," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 222-244.
    8. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    9. Luetkepohl Helmut & Xu Fang, 2011. "Forecasting Annual Inflation with Seasonal Monthly Data: Using Levels versus Logs of the Underlying Price Index," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-23, February.
    10. Heidland, Tobias & Jannsen, Nils & Groll, Dominik & Kalweit, René & Boockmann, Bernhard, 2021. "Analyse und Prognose von Migrationsbewegungen," Kieler Beiträge zur Wirtschaftspolitik 34, Kiel Institute for the World Economy (IfW Kiel).
    11. Danny Lo, 2015. "Essays in Market Microstructure and Investor Trading," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 22, July-Dece.
    12. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    13. Danny Lo, 2015. "Essays in Market Microstructure and Investor Trading," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2015, January-A.

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    More about this item

    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

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