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Forecasting the levels of vector autoregressive log-transformed time series

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  • Arino, Miguel A.
  • Franses, Philip Hans

Abstract

In this paper we give explicit expressions for the forecasts of levels of a vector time series when such forecasts are generated from (possibly cointegrated) vector autoregressions for the corresponding log-transformed time series. We also show that simply taking exponentials of forecasts for logged data leads to substantially biased forecasts. We illustrate this using a bivariate cointegrated vector series containing US GNP and investments.
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  • 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.
    • Handle: RePEc:eee:intfor:v:16:y:2000:i:1:p:111-116
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    1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    2. Dufour, Jean-Marie, 1985. "Unbiasedness of Predictions from Etimated Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 1(3), pages 387-402, December.
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    1. 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.
    2. 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.
    3. Vijay Viswanathan & Linda D. Hollebeek & Edward C. Malthouse & Ewa Maslowska & Su Jung Kim & Wei Xie, 2017. "The Dynamics of Consumer Engagement with Mobile Technologies," Service Science, INFORMS, vol. 9(1), pages 36-49, March.
    4. Fok, Dennis & Franses, Philip Hans, 2001. "Forecasting market shares from models for sales," International Journal of Forecasting, Elsevier, vol. 17(1), pages 121-128.
    5. Franses, Philip Hans, 2006. "Forecasting in Marketing," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 18, pages 983-1012, Elsevier.
    6. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    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. Holtrop, Niels & Wieringa, Jakob & Gijsenberg, Maarten & Stern, P., 2016. "Competitive reactions to personal selling," Research Report 16004-MARK, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    10. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    11. E. A. Fedorova & D. D. Airapetyan & S. O. Musienko & D. O. Afanas’ev & F. Yu. Fedorov, 2018. "Influence of Import Substitution Policy on the Industrial Production Level in Russia: Sector-Specific Issues," Studies on Russian Economic Development, Springer, vol. 29(2), pages 167-173, March.
    12. Cheick Kader M’baye, 2023. "Fertility, employment, and the demographic dividend in sub-Saharan African countries with incipient demographic transition: evidence from Mali," Journal of Population Research, Springer, vol. 40(2), pages 1-15, June.
    13. Jan G. de Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Tinbergen Institute Discussion Papers 05-068/4, Tinbergen Institute.
    14. Bårdsen, Gunnar & Lütkepohl, Helmut, 2011. "Forecasting levels of log variables in vector autoregressions," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1108-1115, October.
    15. Laing, Andrew R. & Nolan, James F., 2009. "Price Dynamics and Market Structure in Transportation: For-Hire Grain Trucking Along the Alberta- Saskatchewan Border," 50th Annual Transportation Research Forum, Portland, Oregon, March 16-18, 2009 207599, Transportation Research Forum.
    16. Salmanzadeh-Meydani, N. & Fatemi Ghomi, S.M.T., 2019. "The causal relationship among electricity consumption, economic growth and capital stock in Iran," Journal of Policy Modeling, Elsevier, vol. 41(6), pages 1230-1256.
    17. 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.
    18. 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.
    19. repec:bny:wpaper:0085 is not listed on IDEAS
    20. Wieringa, Jaap E. & Horvath, Csilla, 2005. "Computing level-impulse responses of log-specified VAR systems," International Journal of Forecasting, Elsevier, vol. 21(2), pages 279-289.
    21. 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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