The connectedness approach is a popular framework for understanding the transmission of shocks across assets or economic variables. It is typically based on the variance decomposition of a vector autoregressive (VAR) model, which measures how much of the forecast error variance of one variable is explained by shocks to others.
While widely used, interpretation of connectedness measures requires care—especially in financial contexts where correlations (signed relationships) often guide investment and risk management decisions.
2. Variance vs. Correlation: Why the Sign Matters
Variance and covariance are inherently unsigned measures of association. They capture the magnitude of dependence, but not its direction. In contrast, correlation provides a signed indicator of whether assets tend to move together (positive correlation) or in opposite directions (negative correlation).
As a result, connectedness metrics—being variance-based—do not distinguish between risk comovement and hedging (safe-haven) behavior.
For example:
A strong stock–gold connectedness does not necessarily imply risk transmission. Gold may act as a safe haven, moving inversely with stocks during crises.
Similarly, stock–bond or stock–uncertainty pairs often exhibit negative correlations. Without considering the expected sign, high connectedness could be misinterpreted as contagion, when it may actually reflect diversification.
3. When Connectedness Makes Sense
The connectedness approach is most interpretable when applied to systems of similar assets, where the underlying economic drivers are expected to move them in the same direction in response to shocks.
Typical examples include:
Multiple cryptocurrencies
Equity indices across markets
Interest rate or credit spread series within the same region
In such systems, a high degree of connectedness genuinely indicates risk propagation and systemic linkages.
Interpretation Caution
Despite opposite correlations, both systems can show similar connectedness magnitudes.
Always consider the theoretical sign of relationships when interpreting results.
4. Recommendations
Use the connectedness approach only when the system variables have theoretically consistent relationships.
Avoid mixing assets with fundamentally opposite expected signs (e.g., stock–gold) unless you explicitly address sign effects.
Consider supplementing variance-based connectedness with correlation or coherence analysis to capture directionality.
Always interpret connectedness in the context of economic theory and empirical sign expectations.
Important
This limitation applies to all its variants, including asymmetric, quantile, time-varying parameter (TVP), R², and R² quantile connectedness measures.
---title: "Connectedness Approach in Financial Systems"date: 2026-01-29categories: [connectedness, econometrics]tags: [VAR, variance-decomposition, correlation, systemic-risk, R]format: html: toc: true code-fold: false code-tools: trueexecute: echo: true eval: true message: false warning: false---## 1. IntroductionThe connectedness approach is a popular framework for understanding the transmission of shocks across assets or economic variables. It is typically based on the **variance decomposition** of a vector autoregressive (VAR) model, which measures how much of the forecast error variance of one variable is explained by shocks to others.While widely used, interpretation of connectedness measures requires care—especially in financial contexts where correlations (signed relationships) often guide investment and risk management decisions.## 2. Variance vs. Correlation: Why the Sign MattersVariance and covariance are inherently **unsigned** measures of association. They capture the *magnitude* of dependence, but not its direction.In contrast, **correlation** provides a signed indicator of whether assets tend to move together (positive correlation) or in opposite directions (negative correlation).As a result, connectedness metrics—being variance-based—do not distinguish between risk comovement and hedging (safe-haven) behavior.For example:- A strong **stock–gold** connectedness does not necessarily imply risk transmission.Gold may act as a safe haven, moving inversely with stocks during crises.- Similarly, **stock–bond** or **stock–uncertainty** pairs often exhibit negative correlations.Without considering the expected sign, high connectedness could be misinterpreted as contagion, when it may actually reflect diversification.## 3. When Connectedness Makes SenseThe connectedness approach is most interpretable when applied to systems of similar assets, where the underlying economic drivers are expected to move them in the same direction in response to shocks.Typical examples include: - Multiple **cryptocurrencies** - **Equity indices** across markets - **Interest rate** or **credit spread** series within the same regionIn such systems, a high degree of connectedness genuinely indicates **risk propagation** and **systemic linkages**.### Interpretation Caution Despite opposite correlations, both systems can show similar connectedness magnitudes. Always consider the theoretical **sign of relationships** when interpreting results.## 4. Recommendations- Use the connectedness approach only when the system variables have theoretically consistent relationships.- Avoid mixing assets with fundamentally opposite expected signs (e.g., stock–gold) unless you explicitly address sign effects.- Consider supplementing variance-based connectedness with correlation or coherence analysis to capture directionality.- Always interpret connectedness in the context of economic theory and empirical sign expectations.### ImportantThis limitation applies to **all** its variants, including **asymmetric**, **quantile**, **time-varying parameter (TVP)**, **R²**, and **R² quantile** connectedness measures.## Minimal Demo of Note```{r}set.seed(123)library(zoo)library(ConnectednessApproach)# -------------------------------# Positive correlation case# -------------------------------n <-1000idx <-seq(as.Date("2010-01-01"), by ="day", length.out = n)x <-rnorm(n)y <-0.5* x +rnorm(n, 0, 0.2)df_p <-zoo(cbind(x, y), order.by = idx)fit_p <-VAR(df_p, configuration =list(nlag =4, method ="pearson"))dca_p <-TimeConnectedness(Phi = fit_p$B,Sigma = fit_p$Q,nfore =10,generalized =TRUE)# Correlationcor(df_p[, 1], df_p[, 2])# Connectedness tableknitr::kable(dca_p$TABLE)# -------------------------------# Negative correlation case# -------------------------------y <--0.5* x +rnorm(n, 0, 0.2)df_n <-zoo(cbind(x, y), order.by = idx)fit_n <-VAR(df_n, configuration =list(nlag =4, method ="pearson"))dca_n <-TimeConnectedness(Phi = fit_n$B,Sigma = fit_n$Q,nfore =10,generalized =TRUE)# Correlationcor(df_n[, 1], df_n[, 2])# Connectedness tableknitr::kable(dca_n$TABLE)```