Uniform Inference with Time Series: Persistence

Programme(s): HORIZON.1.1 - European Research Council (ERC)

Topic(s): ERC-2023-STG - ERC STARTING GRANTS

Call for proposal: ERC-2023-STG

Funding Scheme: HORIZON-ERC - HORIZON ERC Grants

Grant agreement ID: 101117032

Objective: 
This project proposes a novel econometric approach suited for hypothesis testing and confidence interval construction in the presence of generic time series regressors with arbitrary persistence degree. The project will develop inference for a large class of regressor processes commonly encountered in macroeconomic and financial data, ranging from stationary, local-to-unit-root, explosive, long memory, time-varying parameter and other nonstationary processes as well as multivariate systems containing mixed components. The key idea behind the approach is to build a new explanatory variable from the data which conforms to a standard central limit theory even when the original regressor does not. The resulting instrumental variable estimators based on this endogenously constructed instrument are shown to be asymptotically mixed-Gaussian regardless of the true stochastic nature of the regressor, implying standard inference for any IV-based self-normalised test. The main contribution of the project is to place a large class of nonstandard processes with a wide range of dynamics and memory properties under a common econometric framework which delivers standard inference regardless of the regressor's stochastic properties. The asymptotic development of the procedure requires fundamental theoretical contributions such as a novel Granger-Johansen type representation theory for multivariate time series with mixed stochastic components and the asymptotic analysis of time series with different persistence types. The novel procedure is shown to be valid uniformly across persistence regimes and automatically delivers asymptotically correct inference without a priori knowledge of the regressor's true stochastic nature. In addition to its generality and theoretical coherence, the approach has the added advantage of ease of implementation (with closed-form estimators and tests that employ standard critical values), thus making it suitable for general practical application.