Lower Bounds of Uncertainty of Observations of Macroeconomic Variables and Upper Limits on the Accuracy of Their Forecasts

ArXiv ID: 2408.04644 “View on arXiv”

Authors: Unknown

Abstract

This paper defines theoretical lower bounds of uncertainty of observations of macroeconomic variables that depend on statistical moments and correlations of random values and volumes of market trades. Any econometric assessments of macroeconomic variables have greater uncertainty. We consider macroeconomic variables as random that depend on random values and volumes of trades. To predict random macroeconomic variables, one should forecast their probabilities. Upper limits on the accuracy of the forecasts of probabilities of macroeconomic variables, prices, and returns depend on the number of predicted statistical moments. We consider economic obstacles that limit by the first two the number of predicted statistical moments. The accuracy of any forecasts of probabilities of random macroeconomic variables, prices, returns, and market trades doesn’t exceed the accuracy of Gaussian approximations. Any forecasts of macroeconomic variables have uncertainty higher than one determined by predictions of coefficients of variation of random values and volumes of trades.

Keywords: Econometric uncertainty, Statistical moments, Macro forecasting, Gaussian approximations, Market microstructure, Macroeconomic variables

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper relies heavily on advanced probability theory and statistical moment derivations to establish theoretical lower bounds of uncertainty, but presents no empirical backtesting, datasets, or implementation details.

  flowchart TD
    A["Research Goal:<br>Define Uncertainty Lower Bounds<br>& Forecast Accuracy Limits"] --> B["Methodology<br>Stochastic Modeling of<br>Macroeconomic Variables"]

    B --> C["Key Assumptions:<br>Variables depend on<br>Random Values & Trade Volumes"]
    B --> D["Computational Process:<br>Derive Theoretical Bounds<br>based on Statistical Moments & Correlations"]

    C --> E["Data Inputs:<br>Statistical Moments<br>(Mean, Variance, etc.)<br>Market Trade Volumes"]
    D --> F["Modeling Constraints:<br>Limited to First 2 Moments<br>(Gaussian Approximation)"]

    E --> G{"Outcome"}
    F --> G

    G --> H["Key Findings"]
    subgraph H [" "]
        I["Observation Uncertainty<br>has a defined lower bound"]
        J["Forecast Accuracy of Probabilities<br>is upper-limited by Gaussian models"]
        K["Forecast Uncertainty > Uncertainty<br>of Coefficients of Variation"]
    end