Theoretical Economics as Successive Approximations of Statistical Moments

TL;DR

This paper explores how macroeconomic variables and market statistics are interconnected through successive approximations of statistical moments, emphasizing the limitations of current risk measures and the importance of understanding long-term averaging effects.

Contribution

It introduces a framework viewing theoretical economics as a series of successive approximations of statistical moments, linking market trade variables to macroeconomic descriptions over increasing time scales.

Findings

Market trade and return properties depend on trade values and volumes.

Long-term averages exhibit random behaviors described by secondary averaging.

Gaussian distributions limit future market probability predictions.

Abstract

This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval {\Delta} results in the random properties of price and return. We describe how averages and volatilities of price and return depend on the averages, volatilities, and correlations of market trade values and volumes. The averages, volatilities, and correlations of market trade, price, and return can behave randomly during the long interval {\Delta}2>>{\Delta}. To describe their statistical properties during the long interval {\Delta}2, we introduce the secondary averaging procedure of trade, price, and return. We explain why, in the coming years, predictions of market-based probabilities of price and return will be limited by Gaussian distributions. We discuss the roots of the internal weakness of the commonly used hedging tool, Value-at-Risk, that cannot be solved and remains the source of additional risks and losses. One should consider theoretical economics as a set of successive approximations, each of which describes the next array of the n-th statistical moments of market trades, price, return, and macroeconomic variables, which are repeatedly averaged during the sequence of increasing time intervals.