Network log-ARCH models for forecasting stock market volatility

Paper: arXiv 2303.11064

Authors: Raffaele Mattera, Philipp Otto

Abstract

This paper presents a novel dynamic network autoregressive conditional heteroscedasticity (ARCH) model based on spatiotemporal ARCH models to forecast volatility in the US stock market. To improve the forecasting accuracy, the model integrates temporally lagged volatility information and information from adjacent nodes, which may instantaneously spill across the entire network. The model is also suitable for high-dimensional cases where multivariate ARCH models are typically no longer applicable. We adopt the theoretical foundations from spatiotemporal statistics and transfer the dynamic ARCH model for processes to networks. This new approach is compared with independent univariate log-ARCH models. We could quantify the improvements due to the instantaneous network ARCH effects, which are studied for the first time in this paper. The edges are determined based on various distance and correlation measures between the time series. The performances of the alternative networks’ definitions are compared in terms of out-of-sample accuracy. Furthermore, we consider ensemble forecasts based on different network definitions.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper innovatively translates spatiotemporal ARCH models to financial networks to capture instantaneous volatility spillovers in high dimensions. It demonstrates solid empirical rigor through out-of-sample backtesting, ensemble forecasting, and various network structure comparisons.

Research Flowchart

  flowchart TD
    A["Research Goal: Forecast High-Dimensional US Stock Volatility via Network Log-ARCH"] --> B["Data Inputs: US Stock Market Time Series & Network Edge Definitions"]
    B --> C["Edge Construction: Distance & Correlation Measures Between Series"]
    C --> D["Model Development: Integrate Temporal Lagged Volatility & Instantaneous Network Spillovers"]
    D --> E["Model Estimation & Ensemble Forecasting: Individual & Combined Network Specifications"]
    E --> F["Evaluation: Out-of-Sample Accuracy vs. Univariate Log-ARCH Models"]
    F --> G["Key Outcomes: Instantaneous Network Effects Identified & Forecasting Accuracy Improved"]