Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models

ArXiv ID: 2305.06704 “View on arXiv”

Authors: Unknown

Abstract

In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.

Keywords: Time Series Analysis, Lead-Lag Relationships, Clustering, Spectral Clustering, Multivariate Analysis, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like multireference alignment and nonlinear similarity measures, pushing math complexity above the middle threshold. Empirically, it includes extensive experiments with synthetic data, detailed financial market backtesting with trading strategies, and real-world environmental data application, demonstrating high implementation and validation rigor.

  flowchart TD
    A["Research Goal:<br>Detect Lead-Lag Relationships<br>in Lagged Multi-Factor Models"] --> B["Input: Multivariate Time Series"]
    B --> C["Step 1: Feature Extraction<br>Sliding Window Subsequences"]
    C --> D["Step 2: Clustering<br>K-Means++ / Spectral Clustering"]
    D --> E["Step 3: Robust Aggregation<br>Lead-Lag Estimation<br>Across Clusters"]
    E --> F["Outcome: Identifiable<br>Lead-Lag Relationships"]
    F --> G["Application Domains:<br>Financial Markets &<br>Environmental Data"]