 Forecasting Levels in Loglinear Unit Root ModelsEconometric Reviews, 2023, vol. 42, issue 9-10, 780-805 Abstract: This article considers unbiased prediction of levels when data series are modeled as a random walk with drift and other exogenous factors after taking natural logs. We derive the unique unbiased predictors for growth and its variance. Derivation of level forecasts is more involved because the last observation enters the conditional expectation and is highly correlated with the parameter estimates, even asymptotically. This leads to conceptual questions regarding conditioning on endogenous variables. We prove that no conditionally unbiased forecast exists. We derive forecasts that are unconditionally unbiased and take into account estimation uncertainty, non linearity of the transformations, and the correlation between the last observation and estimate, which is quantitatively more important than estimation uncertainty and future disturbances together. The exact unbiased forecasts are shown to have lower Mean Squared Forecast Error (MSFE) than usual forecasts. The results are applied to Bitcoin price levels and a disaggregated eight sector model of UK industrial production. Date: 2023 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:emetrv:v:42:y:2023:i:9-10:p:780-805 Ordering information: This journal article can be ordered from DOI: 10.1080/07474938.2023.2224175 Access Statistics for this article Econometric Reviews is currently edited by Dr. Essie Maasoumi More articles in Econometric Reviews from Taylor & Francis Journals |
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