Global Markets on the Move: How U.S. Economic Shifts Ripple Worldwide

Author: Denis Avetisyan

A new analysis reveals how capturing the full distribution of stock returns across international markets improves our understanding of macroeconomic dependencies and the effects of monetary policy.

The depicted relationship demonstrates that the one factor exhibits a strong inverse correlation with the VIX index, suggesting its potential as a leading indicator of market volatility-as the one factor increases, the VIX tends to decrease, and vice versa.

This paper develops a functional VAR model using cross-sectional distributions from 15 global markets to analyze macroeconomic dependence, monetary policy impacts, and improve forecasting accuracy.

While conventional macroeconomic modeling often relies on aggregated market indices, it overlooks potentially crucial information embedded within the cross-sectional behavior of global stock returns. This is addressed in ‘U.S. Economy and Global Stock Markets: Insights from a Distributional Approach’, which introduces a novel functional vector autoregressive (VAR) framework to jointly model U.S. macroeconomic indicators and the evolving distributions of returns from fifteen international markets. The analysis reveals that capturing higher-order distributional features-specifically kurtosis-not only improves macroeconomic forecasting but also unveils a previously unobserved channel through which contractionary monetary policy impacts global financial markets. Could a more nuanced understanding of cross-sectional dependencies ultimately provide policymakers with more effective tools for navigating an increasingly interconnected global economy?

Unveiling the Patterns of Financial Interdependence

The pursuit of precise financial modeling isn’t merely an academic exercise, but a fundamental necessity for navigating the intricacies of modern global markets. Effective risk management, from hedging investment portfolios to assessing systemic vulnerabilities, hinges on the ability to anticipate how various economic factors – interest rates, inflation, geopolitical events, and investor sentiment – interact to influence asset prices. Moreover, accurate forecasting allows institutions and policymakers to make informed decisions, allocating capital efficiently and mitigating potential crises. A failure to capture these complex interdependencies can lead to underestimated risks, flawed investment strategies, and ultimately, significant financial losses; therefore, ongoing research focuses on developing more robust and dynamic models that reflect the ever-changing landscape of international finance.

Conventional econometric techniques, while foundational to financial analysis, frequently fall short when attempting to model the dynamic complexities of modern markets. These methods often rely on assumptions of linearity and constant relationships between variables, failing to account for the shifting correlations and evolving patterns observed in asset prices and macroeconomic indicators. The financial world is characterized by feedback loops, behavioral biases, and external shocks – factors that introduce non-linearities and time-varying parameters. Consequently, models built on static assumptions can produce inaccurate forecasts and underestimate risk, particularly during periods of market stress or structural change. Researchers are increasingly turning to more flexible techniques, such as time-varying parameter models and machine learning algorithms, to better capture these nuanced relationships and improve the predictive power of financial models.

Financial returns rarely conform to the bell curve assumptions of traditional statistical models; instead, they exhibit characteristics like volatility clustering – periods of calm punctuated by sudden, dramatic shifts – and asymmetry, where negative returns tend to be larger and more frequent than positive ones. Consequently, standard analytical tools, reliant on normal distributions, often underestimate risk and fail to accurately predict market behavior. Researchers are increasingly turning to sophisticated techniques, such as generalized autoregressive conditional heteroskedasticity (GARCH) models and those employing stable distributions with parameters allowing for skewness and kurtosis, to better capture these features. These advanced methods aim to provide a more realistic representation of market dynamics, acknowledging that $P(x < 0) \neq P(x > 0)$ and that the probability of extreme events is significantly higher than predicted by normal distributions, ultimately leading to improved risk management and forecasting capabilities.

A Functional Framework for Dynamic Financial Analysis

The Functional Vector Autoregression (FunctionalVAR) model represents an advancement over traditional Vector Autoregression (VAR) by accommodating functional data as inputs. Standard VAR models are limited to analyzing multivariate time series of scalar variables; FunctionalVAR extends this capability to include data that evolves continuously over time, such as yield curves or entire time series of economic indicators rather than single point observations. This is achieved by representing these functional variables as infinite-dimensional vectors and applying the principles of functional data analysis within the VAR framework. Consequently, FunctionalVAR allows for a more nuanced and complete representation of economic variables and their interrelationships, potentially capturing dynamic patterns not discernible in scalar VAR models. The model utilizes functional principal component analysis or similar dimensionality reduction techniques to manage the infinite dimensionality of the functional data, enabling computationally feasible estimation and inference.

The Functional Vector Autoregression (FunctionalVAR) model assesses the interdependencies between macroeconomic factors and stock market returns by jointly modeling the Federal Funds Rate, Industrial Production, Trade Balance, and a measure of stock market performance. This simultaneous analysis differs from univariate or bivariate approaches by considering the dynamic feedback loops between all four variables. Specifically, the model estimates the influence of each indicator on the others, allowing for the identification of leading, lagging, and contemporaneous relationships. The inclusion of multiple indicators facilitates a more holistic understanding of market dynamics, as changes in one variable are considered in the context of movements in all others. The resulting parameter estimates quantify the magnitude and direction of these relationships, providing insights into the drivers of stock market fluctuations and the broader economic environment.

Traditional time series analysis of macroeconomic indicators often relies on aggregated data, potentially obscuring nuanced relationships and intraday dynamics. The integration of functional data-representing variables as continuous curves rather than single point estimates-allows the FunctionalVAR model to capture a more complete depiction of these relationships. This approach acknowledges that economic variables evolve over time and are not static, enabling the model to identify lead-lag relationships and co-movements that might be missed by conventional methods. Specifically, functional data analysis techniques, such as principal component analysis applied to the functional observations, can extract key features and reduce dimensionality while preserving the temporal information inherent in the data. The result is a more granular and comprehensive understanding of how macroeconomic factors interact with stock market performance, improving the accuracy and interpretability of model results.

FunctionalVAR facilitates conditional forecasting by allowing for the simulation of multiple potential economic trajectories, or scenarios, based on varying initial conditions and exogenous shocks. This capability moves beyond point forecasts to generate forecast distributions conditioned on specific scenarios, enabling a more nuanced understanding of potential outcomes. By assessing model performance across these diverse scenarios, the accuracy of forecasts is improved, particularly in periods of economic volatility or structural change. The model quantifies the uncertainty associated with forecasts, providing risk measures and confidence intervals for decision-making, and allowing users to evaluate the sensitivity of predictions to changes in underlying economic factors.

Decoding Market Responses Through Impulse Analysis

Impulse Response Functions (IRFs) generated from the FunctionalVAR model quantify the dynamic impact of exogenous shocks to the financial system. Specifically, these functions trace the response of multiple financial variables-including stock market returns, bond yields, and macroeconomic indicators-over time following a one-time, unanticipated disturbance, such as a change in monetary policy or an oil price shock. The FunctionalVAR approach, unlike traditional VAR models, allows for the estimation of responses across a continuous spectrum of variables, providing a more granular understanding of shock propagation. The resulting IRFs demonstrate the magnitude, persistence, and direction of effects, revealing how initial shocks transmit through interconnected financial markets and ultimately influence broader economic conditions. For instance, a positive monetary policy shock may initially decrease interest rates, leading to increased asset prices and economic activity, with the effects gradually dissipating over subsequent periods as captured by the decaying IRF curves.

The FunctionalVAR model demonstrates significant interconnectedness within financial markets by quantifying the impact of macroeconomic shocks on stock market returns. Specifically, the model captures how deviations in key macroeconomic indicators – such as inflation, interest rates, and industrial production – propagate through the financial system and ultimately affect equity valuations. This is achieved through a time-varying parameter structure, allowing the relationships between macroeconomic variables and stock returns to evolve dynamically. Empirical results indicate that shocks to these indicators generate statistically significant and economically meaningful responses in stock market returns, with the magnitude and persistence of these responses varying over time and across different markets. The model’s ability to capture these dynamic interdependencies provides a more realistic and accurate representation of financial market behavior compared to traditional, static models.

The Skew $t$ distribution was implemented to more accurately model the non-normal characteristics of asset returns. Financial data frequently exhibits asymmetry, where negative returns are more likely or have a larger magnitude than positive returns, and heavy tails, indicating a higher probability of extreme events compared to a normal distribution. The Skew $t$ distribution extends the standard $t$ distribution by introducing a skewness parameter, allowing it to model these asymmetrical return distributions. This is achieved through the addition of a shape parameter, $\gamma$, which controls the degree of asymmetry, and a scale parameter, $\lambda$, which controls the heaviness of the tails. By capturing these features, the Skew $t$ distribution provides a more realistic representation of return distributions than models assuming normality, improving the accuracy of statistical inference and forecasting exercises.

Analysis indicates that incorporating the distributional characteristics of global stock markets into a macroeconomic framework yields demonstrably improved forecasting accuracy. This improvement is quantified through the Average Log Predictive Likelihood (ALPL) metric, which assesses the model’s ability to predict future observations. Results show that the mvfVAR model, leveraging these distributional features, consistently outperforms both standard VAR and sktVAR models in density forecasting, as evidenced by higher ALPL scores. This suggests that accounting for non-normal characteristics – such as skewness and kurtosis – present in stock market returns is crucial for enhancing the predictive power of macroeconomic models and improving risk management strategies.

Decomposition of stock market returns via a Fourier Basis allows for the identification of dominant cyclical patterns and their corresponding frequencies. This technique expresses the return series as a sum of sine and cosine waves, each representing a specific frequency component. Analysis of the resulting Fourier coefficients reveals the amplitude and phase of these cycles, quantifying their contribution to overall return variation. The process effectively separates the data into its constituent frequencies, highlighting low-frequency trends, medium-term cycles, and high-frequency noise. By examining the spectral density-the distribution of power across frequencies-researchers can pinpoint statistically significant cycles and gain insights into the underlying drivers of market behavior, independent of specific time-domain characteristics. $R(t) = \sum_{k=0}^{N} a_k \cos(2\pi k t/T) + b_k \sin(2\pi k t/T)$ represents the fundamental form of this decomposition, where $R(t)$ is the return series, and $a_k$ and $b_k$ are the coefficients for cosine and sine waves, respectively.

Implications for Navigating a Complex Financial Landscape

Analysis of stock returns reveals a critical insight: risk is not evenly spread throughout the market. Traditional models often assume a uniform distribution of risk, yet empirical evidence consistently demonstrates that certain assets exhibit significantly higher vulnerability to losses than others. This cross-sectional disparity in risk profiles necessitates a more granular approach to portfolio management, moving beyond broad market averages and focusing on the unique characteristics of individual stocks. Ignoring this heterogeneity can lead to underestimation of potential downside risk and, consequently, suboptimal investment outcomes. Consequently, accurately mapping the distribution of risk across assets-identifying those prone to extreme movements-is paramount for constructing resilient portfolios and effectively mitigating financial exposure, allowing for more targeted hedging strategies and a more precise assessment of potential losses.

Accurate modeling of market volatility and asymmetry represents a cornerstone of effective financial risk management and portfolio construction. Traditional models often assume symmetrical return distributions and constant volatility, failing to capture the pronounced ‘fat tails’ and clustering observed in real-world financial data. This limitation can lead to significant underestimation of potential losses during periods of market stress. Sophisticated techniques that account for these characteristics – such as those employing time-varying volatility and skewness – enable a more realistic assessment of risk exposure. Consequently, investors can construct portfolios that are better aligned with their risk tolerance and achieve more stable returns, while risk managers can implement more effective hedging strategies and capital allocation policies. The ability to anticipate and quantify extreme events, facilitated by these advanced models, is particularly crucial in a global financial landscape increasingly susceptible to unexpected shocks and systemic risk.

Analysis using the Root Mean Squared Forecast Error (RMSFE) reveals a consistent advantage for the mvfVAR model in predicting extreme market behavior. Specifically, mvfVAR demonstrates superior accuracy in forecasting both lower and upper quantile scores – the tails of the return distribution where the most significant risks and opportunities reside. This enhanced predictive capability is crucial because traditional models often struggle to accurately capture these extreme events, leading to underestimated risk exposure and potentially flawed investment decisions. The consistent outperformance of mvfVAR suggests a more reliable framework for anticipating and managing the financial consequences of unexpected market shifts, offering a valuable tool for investors seeking to protect capital and maximize returns even during periods of high volatility.

Analysis of factor loadings revealed substantial explained variance, indicating that the complex dynamics of financial markets can be effectively represented by a limited number of underlying factors. R-squared values consistently demonstrated a significant proportion of variability accounted for by these initial factors, suggesting a low-dimensional structure within the data. Importantly, the identification of clear “elbow points” in both scale and skewness parameters further validated this finding; these points signify a natural cutoff where the addition of further factors yields diminishing returns in explanatory power. This simplification not only enhances the interpretability of the model but also improves its efficiency, allowing for more focused risk assessment and portfolio optimization strategies without sacrificing predictive accuracy.

The study establishes a novel framework for deciphering market dynamics by converging functional data analysis with sophisticated statistical methodologies. Rather than treating assets as isolated points, this approach views them as continuous functions, capturing a richer spectrum of information embedded within their return patterns. This functional perspective, combined with techniques like vector autoregression (VAR), allows for a more holistic representation of interdependencies and a more accurate depiction of volatility and asymmetry. Consequently, the framework delivers improved forecasting capabilities, particularly in predicting extreme market events, and provides a more nuanced understanding of risk distribution across assets – a critical advancement for portfolio construction and effective risk management in complex financial landscapes.

The evolving landscape of global financial markets demands increasingly sophisticated analytical tools, and this research provides a novel framework for understanding and managing risk within that complexity. By leveraging functional data analysis and advanced statistical modeling-specifically the mvfVAR approach-investors are better equipped to forecast extreme market movements and construct more resilient portfolios. Policymakers, too, can benefit from this research, gaining a more nuanced understanding of systemic risk and improving the efficacy of financial regulations. The demonstrated accuracy of mvfVAR in predicting quantile scores-critical for assessing tail risk-offers a tangible advantage in a world where unforeseen events can rapidly destabilize markets, providing a foundation for proactive and informed decision-making in both investment strategies and regulatory oversight.

The study meticulously examines the distributional characteristics of global stock markets, revealing nuances often obscured by traditional macroeconomic analyses. This approach echoes Ludwig Wittgenstein’s assertion: “The limits of my language mean the limits of my world.” Similarly, limiting analytical frameworks to solely focus on mean values can restrict understanding of complex financial dynamics. By incorporating the skew-t distribution and cross-sectional data, the functional VAR model expands the ‘language’ of economic analysis, offering a more complete picture of macroeconomic dependence and the impact of monetary policy. Carefully checking data boundaries to avoid spurious patterns is crucial when working with these distributional features, ensuring the insights gained are genuine reflections of market behavior.

Beyond the Distribution

The exercise of mapping macroeconomic dependence through distributional features of global stock markets inevitably reveals the limits of the map itself. This work demonstrates the value of acknowledging skewness and heavier tails, yet the very act of parameterizing ‘risk’ into a Skew-t distribution implies a static understanding of a fundamentally evolving phenomenon. The next step isn’t simply increasing the complexity of the distributional assumption, but questioning the assumption of a fixed distribution altogether. Are we chasing shadows of predictability, or mistaking the artifact of estimation for a genuine characteristic of the system?

Further investigation should explore non-parametric methods, allowing the cross-sectional distributions to speak for themselves without the constraints of pre-defined functional forms. A particularly intriguing avenue lies in exploring how changes in these distributions precede macroeconomic shifts – not just co-move with them. The functional VAR framework, while powerful, assumes a relatively symmetric relationship; disentangling lead-lag dynamics within the distributional space may reveal hidden asymmetries in global financial integration.

Ultimately, this research underscores a simple, if frustrating, truth: the more rigorously one attempts to quantify systemic risk, the more apparent its qualitative nature becomes. Perhaps the most valuable insight isn’t a more accurate forecast, but a more nuanced appreciation for the inherent unknowability of complex systems. The patterns are there, but they shift, fragment, and recombine, perpetually challenging any attempt at complete capture.

Original article: https://arxiv.org/pdf/2511.17140.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

Unveiling the Patterns of Financial Interdependence

A Functional Framework for Dynamic Financial Analysis

Decoding Market Responses Through Impulse Analysis

Implications for Navigating a Complex Financial Landscape

Beyond the Distribution

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