cointegration time series modeling

This paper addresses the challenge of cointegration testing for high-dimensional vector autoregressive (VAR) models under the joint asymptotic regime where both the cross-sectional dimension (N) and time series length (T) grow large. We propose a novel test grounded in random matrix theory, extending the Johansen likelihood ratio test to the high-dimensional setting. Crucially, we rigorously derive its limiting null distribution as the partial sum of the Airy(_1) point process—bypassing the limitations of conventional low-dimensional asymptotics. Based on this theoretical foundation, we develop an open-source R package and provide critical value tables accurate to three decimal places. Monte Carlo simulations and empirical analysis on real stock market data demonstrate the method’s superior finite-sample performance and statistical power. To our knowledge, this is the first rigorous, computationally feasible, and fully reproducible cointegration test for nonstationary high-dimensional time series.

This paper addresses the challenge of modeling nonlinear and asymmetric dynamic relationships among macroeconomic and financial variables. We propose the first scenario-analysis-oriented, dynamic nonparametric multivariate Bayesian machine learning framework. Methodologically, we adapt classical econometric tools—including conditional forecasting and generalized impulse response analysis—to high-dimensional Bayesian nonparametric models, integrating dynamic factor extensions and Monte Carlo simulation to enable asymmetric shock response estimation and conditional scenario inference. Our key contribution is the first systematic integration of traditional scenario-analysis tools with nonlinear Bayesian machine learning, explicitly capturing structural asymmetry. The framework is validated across three empirical domains: financial stress testing, macroeconomic risk assessment, and cross-border spillover analysis. Results demonstrate substantial improvements in risk measurement accuracy and cross-jurisdictional early-warning capability, offering a novel paradigm for prudential regulation and policy evaluation.

A long-standing open question in nonlinear cointegration concerns how shared nonlinear stochastic trends emerge from nonlinear vector autoregressive (VAR) models. Method: Framing the analysis within the CKSVAR model—driven by occasional constraints such as the zero lower bound on interest rates—we jointly characterize short- and long-run dynamics of time series. Contribution/Results: We extend the Granger–Johansen representation theorem to nonlinear cointegration for the first time, deriving novel unit-root and cointegration-rank criteria tailored to threshold nonlinearity. We further derive new classes of cointegrating trend processes—including controlled, truncated, and kinked Brownian motions. Our theoretical results fully characterize the conditions under which linear and nonlinear common trends arise, demonstrating that CKSVAR supports a substantially richer set of long-run behaviors than linear VAR models. Moreover, the framework establishes a new foundation for structural parameter identification in nonlinear cointegrated systems.

This paper addresses unit root and cointegration inference for functional time series in Hilbert spaces, focusing on identifying the number of common stochastic trends—i.e., the dimension of the nonstationary subspace—and conducting hypothesis tests for the nonstationary and stationary subspaces. We systematically extend classical unit root and cointegration theory to arbitrary-dimensional Hilbert spaces for the first time, proposing a projection-operator spectral analysis method that is asymptotically efficient, fully data-driven (requiring no prior dimension specification), and uniformly applicable to high-dimensional vector time series, dynamic functional factor models, and curve-valued time series. We further develop theoretically grounded dimension-selection criteria and valid test statistics with rigorous asymptotic properties. Empirical applications to the U.S. yield curve and labor market indices robustly identify key common nonstationary trends, demonstrating the method’s interpretability and practical utility for real-world high-dimensional functional time series.

This paper addresses the challenge of identifying specific structural shocks in structural vector autoregressive (SVAR) models using heteroskedasticity alone—without conventional sign or exclusion restrictions. Within a Bayesian framework, we propose a non-centered stochastic volatility approach that dispenses with such auxiliary constraints. Theoretically, we derive necessary and sufficient conditions for partial and global identification of structural parameters. Methodologically, we develop a heteroskedasticity-based statistical identification diagnostic and introduce a shrinkage prior centered at homoskedasticity, ensuring identification is fully data-driven. Empirically, applying the method to a U.S. fiscal structural model, we achieve partial identification of structural shocks without imposing additional identifying restrictions, thereby substantially enhancing estimation robustness and economic interpretability.

Traditional econometric approaches treat observational data as vectors, making it difficult to effectively capture the two-dimensional structure of matrix-valued data and its intrinsic long-run equilibrium relationships. This study proposes a novel matrix cointegrated error correction model that, for the first time, establishes a cointegration framework admitting an equivalent matrix autoregressive (MAR) representation. By preserving the native matrix form of the data, the model naturally accommodates both cointegrating relationships and dynamic adjustment mechanisms. It accurately characterizes long-run equilibria and short-run dynamics among variables while maintaining structural integrity, thereby offering both economic interpretability and methodological innovation.

This study addresses the challenge of jointly modeling volatility spillovers and co-movements in multi-asset settings by proposing a novel Vector Multiplicative Error Model (Vector MEM). The model incorporates a latent variable structure to simultaneously capture cross-asset volatility spillovers and co-movement dynamics, while introducing a model-driven clustering strategy to reduce parameter dimensionality and enhance scalability in high-dimensional contexts. This approach represents the first integration of both mechanisms within the MEM framework, balancing expressive power with computational tractability. Empirical analysis based on 29 Dow Jones constituents demonstrates that the proposed model outperforms or matches existing Vector MEM methods across multiple evaluation metrics, effectively uncovering the transmission pathways and co-movement structure of market volatility.

This study addresses the issue of size distortion in weak exogeneity tests within dynamic linear models, which often arises due to omitted variables inducing reverse causality. To resolve this, the paper proposes a novel asymmetric Portmanteau test that avoids joint dynamic parametrization by constructing an asymmetric quadratic form statistic based on the sequential cross-correlation structure. This statistic effectively distinguishes between violations of weak exogeneity and genuine reverse causal effects, and under the null hypothesis, it follows an asymptotic normal distribution, thereby circumventing the size distortions inherent in conventional symmetric tests. An empirical application to economic policy uncertainty shocks reveals rejection of weak exogeneity; upon introducing control variables, the inflation response shifts from negative to positive, lending support to a supply-shock interpretation and demonstrating the practical utility of the proposed method.