Paper: arXiv 2305.18991

Authors: Andrew J. Patton, Yasin Simsek

Abstract

We propose methods to improve the forecasts from generalized autoregressive score (GAS) models (Creal et. al, 2013; Harvey, 2013) by localizing their parameters using decision trees and random forests. These methods avoid the curse of dimensionality faced by kernel-based approaches, and allow one to draw on information from multiple state variables simultaneously. We apply the new models to four distinct empirical analyses, and in all applications the proposed new methods significantly outperform the baseline GAS model. In our applications to stock return volatility and density prediction, the optimal GAS tree model reveals a leverage effect and a variance risk premium effect. Our study of stock-bond dependence finds evidence of a flight-to-quality effect in the optimal GAS forest forecasts, while our analysis of high-frequency trade durations uncovers a volume-volatility effect.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper effectively combines rigorous statistical modeling (GAS models) with non-parametric machine learning techniques (decision trees and random forests) to overcome dimensionality issues. It demonstrates strong empirical rigor through four diverse financial applications, consistently outperforming baseline models while extracting meaningful economic insights.

Research Flowchart

  flowchart TD
    A[Goal: Improve GAS Model Forecasts via Parameter Localization] --> B[Method: Combine GAS Models with Decision Trees & Random Forests]
    B --> C[Inputs: State Variables & Multi-Asset Time Series Data]
    C --> D[Process: Non-Parametric Partitioning & Multi-Variable Score Tree Estimation]
    D --> E[Outcome: Outperforms Baseline GAS & Avoids Curse of Dimensionality]
    E --> F[Key Empirical Discoveries: Leverage, Flight-to-Quality, & Volume-Volatility Effects]