cointegration testing

This paper addresses the modeling challenge of smoothly evolving shock persistence in economic time series, departing from conventional assumptions of homogeneity or piecewise-constant persistence. Methodologically, it introduces the concept of “dynamic local persistence” and develops a time-varying coefficient framework, integrating local regression with rolling-window estimation to nonparametrically and granularly identify the decay dynamics of shocks. Empirical applications to inflation and stock market volatility reveal pronounced, continuously evolving persistence structures: inflation shock persistence exhibits a systematic decline after the mid-2000s, whereas equity volatility shock persistence markedly increases around the global financial crisis. The proposed framework delivers an interpretable and estimable tool for analyzing heterogeneous macroeconomic policy transmission and dynamic asset risk pricing.

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 jump detection in high-frequency order prices from limit order books corrupted by one-sided (biased) market microstructure noise. Method: We propose the first global jump testing framework tailored to one-sided noise, constructing a test statistic grounded in extreme value theory and rigorously deriving its asymptotic distribution; jump locations are precisely identified via local order statistics, while jump sizes are robustly estimated using pointwise consistent volatility estimation. Contribution/Results: The test is proven consistent with asymptotically optimal convergence rate, breaking the detection lower bound of conventional additive-noise models and substantially enhancing sensitivity to small jumps. Simulation and empirical studies demonstrate superior sensitivity and reliability over state-of-the-art methods, significantly improving intraday order-flow micro-jump detection rates.

This paper addresses the challenges of modeling multivariate joint distributions and accurately assessing tail risk in nonstationary complex systems—such as financial markets—where conventional methods struggle with time-varying dependence and heavy-tailed dynamics. We propose a parsimonious stochastic matrix model that jointly captures the evolution of time-varying correlations and heavy-tailed structures. Leveraging intraday return data from 479 S&P 500 constituents in 2014, we pioneer the integration of random matrix theory with nonstationary time series analysis and heavy-tailed statistical inference. Empirical results demonstrate that nonstationarity intensifies algebraic tail behavior. The model characterizes the dynamic evolution of the multivariate density function across multiple time scales using a minimal set of interpretable parameters, faithfully reproducing tail thickening induced by correlation drift. It significantly improves the accuracy of extreme-risk measurement for multi-asset portfolios.

This paper addresses risk assessment of rare events in nonstationary complex systems, focusing on modeling heavy-tailed multivariate distributions of interdependent variables and elucidating how time-varying dependence amplifies tail risk. We propose a novel class of random matrix models that unifies Gaussian and algebraic heavy-tailed characteristics, deriving—for the first time—closed-form joint distributions and explicit moment expressions. In the algebraic case, the model reduces the number of fitting parameters by one to two, substantially enhancing practicality. The methodology integrates scalar products of generalized correlation matrices, random matrix theory, heavy-tailed distribution modeling, and analytical derivation of joint distributions for linear combinations. Empirical validation on financial data demonstrates high accuracy. The framework provides an interpretable, computationally tractable theoretical foundation for extreme-risk quantification and empirical financial market analysis.

Financial time series exhibit intertwined fast and slow dynamic components that are challenging to disentangle for effective risk modeling and strategy design. This work formalizes the multiscale decomposition problem as a generalized eigenvalue problem, integrating variance and tail stationarity criteria to achieve an interpretable separation of slowly varying and rapidly fluctuating components in asset returns. The proposed method successfully identifies economically meaningful multiscale structures across diverse datasets—including foreign exchange rates, equity ETFs, and government bond yields—thereby substantially enhancing the efficacy of parameter drift detection, mean-reversion modeling, and tail risk management.

Traditional time-varying parameter VAR (TVP-VAR) models suffer from sluggish parameter adaptation, limiting their ability to capture structural breaks during major crises. To address this, we propose the observable-variable-driven adaptive TVP-VAR (AVP-VAR), which employs macroeconomic and financial indicators as exogenous modulators directly mapped to VAR coefficients—replacing the conventional latent-state process. By embedding dynamics into the observation equation, AVP-VAR enables linear, interpretable, and highly parsimonious coefficient estimation. This formulation avoids computationally intensive filtering procedures and mitigates identification issues inherent in latent-factor approaches. Empirical analysis using U.S. and European data demonstrates that AVP-VAR substantially improves out-of-sample forecasting accuracy—particularly during high-volatility episodes—while retaining theoretical simplicity and policy interpretability.

This paper addresses pervasive overfitting and look-ahead bias in algorithmic trading by proposing the first forward-validation framework that simultaneously ensures rigorous statistical validation and full interpretability. Methodologically: (1) it implements a rolling, information-set-constrained forward-testing paradigm across 34 independent periods; (2) integrates hypothesis-driven signal generation (expressed in natural language), market microstructure modeling, and realistic trading constraints; and (3) supports plug-and-play integration of novel hypothesis generators (e.g., LLMs), reinforcement learning, and OHLCV-based feature engineering. Empirical evaluation on 100 U.S. equities from 2015–2024 yields an annualized return of 0.55%, Sharpe ratio of 0.33, maximum drawdown of −2.76%, and beta of just 0.058—demonstrating robust profitability during high-volatility regimes. A non-significant p-value of 0.34 underscores result honesty and reproducibility. The core contribution is establishing a new validation standard that jointly prioritizes statistical rigor and model interpretability.

This study addresses the challenge of improving volatility forecasting in financial markets by integrating long memory, rough volatility, and information persistence. The proposed framework combines semi-parametric long-memory estimation—employing both Geweke–Porter–Hudak and local Whittle methods—with rough volatility diagnostics and a structured HAR-X regression model. Notably, it introduces cross-sectional and industry-level persistence aggregation measures and their interactions with market stress regimes for the first time. Empirical validation across 115 S&P 500 constituents demonstrates significant out-of-sample predictive gains, particularly in long-horizon forecasts and volatility-managed portfolios. These results indicate that volatility persistence conveys incremental economic information beyond conventional risk factors.

This paper addresses the dynamic evolution of conditional dependence structures among macroeconomic variables before and after economic crises (e.g., the Great Recession). To this end, we propose the spOUTAR model—a unified Bayesian framework integrating orthogonal rotation-based univariate time-series latent factors (OUT), sparse precision matrix modeling, and autoregressive dynamics. By sharing parameters across pre- and post-crisis regimes, spOUTAR enables joint Bayesian estimation of stage-specific precision matrices, thereby accurately identifying structural breaks, emergent dependencies, and gradual network reconfigurations. Compared to existing approaches, it offers three key advantages: interpretable high-dimensional covariance structures, statistically robust detection of structural change points, and flexible modeling of nonstationary dependence evolution. Empirical analysis on U.S. and OECD multi-country macroeconomic data demonstrates that spOUTAR effectively captures systemic network transformations induced by the Great Recession, providing a novel analytical tool for studying crisis transmission mechanisms.