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The mean squared prediction error paradox

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  • Pablo Pincheira Brown
  • Nicolás Hardy

Abstract

In this paper, we show that traditional comparisons of mean squared prediction error (MSPE) between two competing forecasts may be highly controversial. This is so because when some specific conditions of efficiency are not met, the forecast displaying the lowest MSPE will also display the lowest correlation with the target variable. Given that violations of efficiency are usual in the forecasting literature, this opposite behavior in terms of accuracy and correlation with the target variable may be a fairly common empirical finding that we label here as “the MSPE paradox.” We characterize “paradox zones” in terms of differences in correlation with the target variable and conduct some simple simulations to show that these zones may be non‐empty sets. Finally, we illustrate the relevance of the paradox with a few empirical applications.

Suggested Citation

  • Pablo Pincheira Brown & Nicolás Hardy, 2024. "The mean squared prediction error paradox," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(6), pages 2298-2321, September.
    • Handle: RePEc:wly:jforec:v:43:y:2024:i:6:p:2298-2321
    DOI: 10.1002/for.3129
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    Cited by:

    1. Nicolás Magner & Nicolás Hardy, 2022. "Cryptocurrency Forecasting: More Evidence of the Meese-Rogoff Puzzle," Mathematics, MDPI, vol. 10(13), pages 1-27, July.
    2. Pablo Pincheira & Nicolas Hardy & Andrea Bentancor, 2022. "A Simple Out-of-Sample Test of Predictability against the Random Walk Benchmark," Mathematics, MDPI, vol. 10(2), pages 1-20, January.
    3. Pablo Pincheira Brown & Nicolás Hardy, 2024. "Correlation‐based tests of predictability," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(6), pages 1835-1858, September.
    4. Pincheira-Brown, Pablo & Bentancor, Andrea & Hardy, Nicolás & Jarsun, Nabil, 2022. "Forecasting fuel prices with the Chilean exchange rate: Going beyond the commodity currency hypothesis," Energy Economics, Elsevier, vol. 106(C).
    5. Shafiullah Qureshi & Ba Chu & Fanny S. Demers, 2021. "Forecasting Canadian GDP Growth with Machine Learning," Carleton Economic Papers 21-05, Carleton University, Department of Economics.
    6. Pablo Pincheira Brown & Nicolás Hardy, 2024. "Correlation‐based tests of predictability," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(6), pages 1835-1858, September.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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