Estimation of market efficiency process within time-varying autoregressive models by extended Kalman filtering approach

ArXiv ID: 2310.04125 “View on arXiv”

Authors: Unknown

Abstract

This paper explores a time-varying version of weak-form market efficiency that is a key component of the so-called Adaptive Market Hypothesis (AMH). One of the most common methodologies used for modeling and estimating a degree of market efficiency lies in an analysis of the serial autocorrelation in observed return series. Under the AMH, a time-varying market efficiency level is modeled by time-varying autoregressive (AR) process and traditionally estimated by the Kalman filter (KF). Being a linear estimator, the KF is hardly capable to track the hidden nonlinear dynamics that is an essential feature of the models under investigation. The contribution of this paper is threefold. We first provide a brief overview of time-varying AR models and estimation methods utilized for testing a weak-form market efficiency in econometrics literature. Secondly, we propose novel accurate estimation approach for recovering the hidden process of evolving market efficiency level by the extended Kalman filter (EKF). Thirdly, our empirical study concerns an examination of the Standard and Poor’s 500 Composite stock index and the Dow Jones Industrial Average index. Monthly data covers the period from November 1927 to June 2020, which includes the U.S. Great Depression, the 2008-2009 global financial crisis and the first wave of recent COVID-19 recession. The results reveal that the U.S. market was affected during all these periods, but generally remained weak-form efficient since the mid of 1946 as detected by the estimator.

Keywords: Adaptive Market Hypothesis (AMH), Extended Kalman filter (EKF), Time-varying autoregressive (AR) process, Weak-form market efficiency, Serial autocorrelation, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques including time-varying autoregressive models, state-space representations, and extended Kalman filtering with parameter estimation via maximum likelihood. It demonstrates high empirical rigor through extensive backtesting on major indices (S&P 500, DJIA) over nearly a century of data, including stress periods like the Great Depression and 2008 crisis.

  flowchart TD
    A["Research Goal<br>Estimate market efficiency<br>via time-varying AR models"] --> B["Data Selection<br>SP500 & DJIA Indices<br>Monthly: Nov 1927 - Jun 2020"]
    
    B --> C["Methodology<br>Extended Kalman Filter EKF<br>vs. Traditional Kalman Filter"]
    
    C --> D{"Computational Process<br>Estimate Time-Varying AR Coefficients"}
    D --> E["Track Hidden Dynamics<br>Nonlinear market efficiency<br>evolution"]
    
    E --> F["Key Findings Outcomes"]
    
    F --> G["U.S. Market Impact<br>Great Depression, 2008-09 Crisis, COVID-19"]
    F --> H["Weak-form Efficiency<br>Established since mid-1946"]
    
    style A fill:#e1f5fe
    style B fill:#f3e5f5
    style C fill:#e8f5e8
    style D fill:#fff3e0
    style E fill:#fce4ec
    style F fill:#e8eaf6
    style G fill:#ffebee
    style H fill:#e0f2f1