Economic Theory as Successive Approximations of Statistical Moments

Author:

Victor Olkhov

Keyword:

Economics, General Economics, General Economics (econ.GN), Statistical Finance (q-fin.ST)

journal:

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date:

2023-09-27 16:00:00

Abstract

This paper highlights the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. We consider economic transactions during the averaging time interval {\Delta} as the exclusive matter that determines the change of any economic variables. We regard the stochasticity of market trade values and volumes during {\Delta} as the only root of the random properties of price and return. We describe how the market-based n-th statistical moments of price and return during {\Delta} depend on the n-th statistical moments of trade values and volumes or equally on sums during {\Delta} of the n-th power of market trade values and volumes. We introduce the secondary averaging procedure that defines statistical moments of trade, price, and return during the averaging interval {\Delta}2>>{\Delta}. As well, the secondary averaging during {\Delta}2>>{\Delta} introduces statistical moments of macroeconomic variables, which were determined as sums of economic transactions during {\Delta}. In the coming years, predictions of the market-based probabilities of price and return will be limited by Gaussian-type distributions determined by the first two statistical moments. We discuss the roots of the internal weakness of the conventional hedging tool, Value-at-Risk, that could not be solved and thus remain the source of additional risks and losses. One should consider economic theory as a set of successive approximations, each of which describes the next array of the n-th statistical moments of market transactions and macroeconomic variables, which are repeatedly averaged during the sequence of increasing time intervals.