Modeling and Analysis of the Lead-Lag Network of Economic Indicators

TL;DR

The paper tackles the problem of identifying lead-lag relationships among economic indicators during the COVID-19 era. It introduces a weighted, directed network framework built on lagged multivariate time series and assesses edge strengths via correlation, mutual information, and transfer entropy, with PageRank used to rank influential and influenced indicators. Key findings show that results are robust within each metric but highly sensitive to the choice of metric, with transfer entropy offering the most consistent and robust rankings. This framework provides a flexible, non-predictive tool for exploring complex time-series interdependencies that can be applied to other domains with multivariate dynamics.

Abstract

We propose a method of analyzing multivariate time series data that investigates lead-lag relationships among economic indicators during the COVID-19 era with a weighted directed network of lagged variables. The analysis includes a stock index, average unemployment, and several variables that are used to calculate inflation. Three complex networks are created, with these variables and several lags of each as the network nodes. Network edges are weighted based on three relationship metrics: correlation, mutual information, and transfer entropy. In each network, nodes are merged, and edges are aggregated to simplify the weighted directed graph. Pagerank is used to determine the most influential and the most influenced node over the time period. Results were reasonably robust within each network, but they were heavily dependent on the choice of metric.

Figures (7)

• Figure 1: Rate of change (y-axis) per variable from July 2019 through December 2022. The y-axis is truncated for visibility, with an off-the-chart value of 197% increase in unemployment from March to April 2020.
• Figure 2: Correlation network. This directed network has edge weights based on Eq. \ref{['eq: weight']} with correlation and parameter $a=1$. This graph has $169$ nodes and $12168$ edges.
• Figure 3: Mutual information network. This directed network has edge weights based on Eq. \ref{['eq: weight']} with mutual information Eq. \ref{['eq: MI']} and parameter $a=1$. This graph has $169$ nodes and $6258$ edges.
• Figure 4: Transfer entropy network. This directed network has edge weights based on Eq. \ref{['eq: weight']} with transfer entropy Eq. \ref{['eq: TE']} and parameter $a=1$. This graph has $169$ nodes and $6610$ edges.
• Figure 5: PR values (y-axis) per node (x-axis) for networks with edge weights based on correlation and determined by select values of $a$ in the legend. The nodes on the x-axis are sorted by average PR. The most influential node is shown on the left and has greatest PR with edges directed toward the lead variable. The most influenced node is shown on the right and has greatest PR with edges directed toward the lagged variable.