Uniform inference with time series

Introduction

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.

Development of Inference

The project will develop inference for a large class of regressor processes commonly encountered in macroeconomic and financial data, including:

1. Stationary processes
2. Local-to-unit-root processes
3. Explosive processes
4. Long memory processes
5. Time-varying parameter processes
6. Other nonstationary processes
7. Multivariate systems containing mixed components

Key Idea

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. This implies standard inference for any IV-based self-normalized test.

Main Contribution

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. This framework delivers standard inference regardless of the regressor's stochastic properties.

Theoretical Contributions

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
• The asymptotic analysis of time series with different persistence types

Validity and Implementation

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, featuring closed-form estimators and tests that employ standard critical values. This makes it suitable for general practical application.