United States Patent

    Otunuga, Olusegun Michael, Gangaram Ladde, Nathan Ladde.

    Local Lagged Adapted Generalized Method of Moments Dynamic Process

    United States Patent No. 10,719,578
    Granted: July 21, 2020

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    Summary of the Patent

    The Local Lagged Adapted Generalized Method of Moments (LLGMM) Dynamic Process is a statistical and computational framework designed to estimate and forecast parameters in complex stochastic dynamic systems. Many real-world systems, such as financial markets, epidemiological processes, energy commodities, and biological systems, are governed by stochastic dynamics where parameters may evolve over time. Traditional estimation methods often struggle to accurately capture such changes.

    This patented method introduces a localized and adaptive extension of the classical Generalized Method of Moments (GMM). The approach incorporates lagged information from observed data and allows parameters to be estimated dynamically using local information. By combining local estimation techniques with lagged moment conditions, the LLGMM framework improves the reliability and stability of parameter estimation in stochastic models.

    Motivation

    Standard statistical estimation techniques frequently assume that model parameters remain constant or that data follow simple deterministic patterns. In many real-world systems, however, parameters vary over time and the underlying dynamics may include delays or lagged effects. These complexities can lead to inaccurate parameter estimates and unreliable forecasts when traditional methods are applied.

    The LLGMM dynamic process addresses these challenges by introducing adaptive estimation techniques that respond to local variations in the data. This allows the method to capture evolving dynamics in stochastic systems more effectively.

    Key Innovation

    • Local estimation: Parameter estimation is performed within localized windows of the dataset rather than globally across all observations.
    • Lagged moment conditions: Past observations are incorporated into the estimation procedure, allowing delayed system effects to be captured.
    • Adaptive updating: Parameter estimates are updated dynamically as new information becomes available.

    Applications

    The LLGMM dynamic process has broad applications across many scientific disciplines, including:

    • Financial econometrics and exchange rate modeling
    • Energy commodity price dynamics
    • Epidemiological modeling of infectious diseases
    • Biostatistical analysis of stochastic biological systems
    • Engineering systems involving dynamic forecasting and control

    Impact

    The LLGMM framework contributes to modern statistical modeling by providing a flexible method for estimating parameters in stochastic dynamic systems where traditional approaches are insufficient. By accounting for lagged dependencies and time-varying parameters, the method enhances forecasting performance and provides improved modeling tools for complex real-world systems.