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This article explores how the choice of lag length affects the ADF test for detecting unit roots in time series data.

Testing for a Unit Root in Time Series With Pretest Data-Based Model Selection

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Randomized trial examines unit root inference in time series, suggesting lag-length selection greatly influences outcomes.

This article explores how the choice of lag length affects the ADF test for detecting unit roots in time series data.
Derived conditions for ADF test distribution convergence under various lag-selection strategies.
Conducted simulations to evaluate ADF test performance based on different lag-length selections.
Applied findings to analyze inventory series for unit root inference sensitivity.
ADF test performance significantly improves with data-driven lag length selection.
Simulation results confirm that many lag-selection methods satisfy necessary convergence conditions.
Real-world application shows that lag-length choice can dramatically affect unit root conclusions.

Alastair R. Hall (1994) studied this question.

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