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

TL;DR

This paper establishes theoretical lower bounds on the uncertainty of macroeconomic variable observations and the upper limits on the accuracy of their forecasts, highlighting fundamental statistical constraints.

Contribution

It introduces a theoretical framework linking macroeconomic observation uncertainty to statistical moments and correlations, and defines upper bounds on forecast accuracy based on these moments.

Findings

Uncertainty of macroeconomic observations depends on statistical moments and correlations.

Forecast accuracy is limited by the number of predicted moments and Gaussian approximation bounds.

Forecasts cannot surpass the uncertainty dictated by the coefficients of variation of underlying variables.

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.