Theoretical Economics as Successive Approximations of Statistical Moments

Olkhov, Victor (2023): Theoretical Economics as Successive Approximations of Statistical Moments.

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 Δ 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 Δ2>>Δ. To describe their statistical properties during the long interval Δ2, 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: theoretical economics; average and volatility; price and return; market-based probability
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E17 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation

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