Theoretical Economics as Successive Approximations of Statistical Moments

ArXiv ID: 2310.05971 “View on arXiv”

Authors: Unknown

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.

Keywords: Statistical Moments, Market Microstructure, Value-at-Risk (VaR), Macroeconomic Variables, Price Dynamics, General Markets

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats
• Why: The paper relies on heavy mathematical notation involving statistical moments and successive approximations, but it lacks backtest-ready implementation details, specific datasets, or empirical validation, focusing instead on theoretical frameworks.

  flowchart TD
    A["Research Goal:<br>Link Macro Variables to<br>Microstructure Statistical Moments"] --> B
    B["Methodology:Sequential Averaging & Approximation"] --> C
    C["Input:Market Trades<br>(Values, Volumes)"] --> D
    D["Process 1:<br>Averaging over interval Δ"] --> E
    E["Output 1:<br>Random Price & Return<br>with moments dependent on trade moments"] --> F
    F["Process 2:<br>Secondary Averaging over interval Δ2 >> Δ"] --> G
    G["Key Findings & Outcomes:<br>1. Limitation of Gaussian predictions<br>2. Internal weakness of VaR<br>3. Theory as successive approximations of n-th moments"]