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Economic Theory as Successive Approximations of Statistical Moments

Olkhov, Victor (2023): Economic Theory as Successive Approximations of Statistical Moments.

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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 Δ as the exclusive matter that determines the change of any economic variables. We regard the stochasticity of market trade values and volumes during Δ 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 Δ depend on the n-th statistical moments of trade values and volumes or equally on sums during Δ 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 Δ2>>Δ. As well, the secondary averaging during Δ2>>Δ introduces statistical moments of macroeconomic variables, which were determined as sums of economic transactions during Δ. 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.

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