Bootstrap Adaptive Lasso Solution Path Unit Root Tests

TL;DR

This paper introduces bootstrap methods for adaptive Lasso unit root tests to enhance finite-sample accuracy and applicability in non-stationary volatility contexts, with empirical application to Eurozone housing prices.

Contribution

It develops sieve wild bootstrap analogues for adaptive Lasso unit root tests, improving finite-sample properties and extending applicability to models with time-varying volatility.

Findings

Bootstrap reduces size distortions in tests.

Evidence of period-specific stationarity in Eurozone housing prices.

Bootstrap enhances test accuracy in non-stationary volatility environments.

Abstract

We propose sieve wild bootstrap analogues to the adaptive Lasso solution path unit root tests of Arnold and Reinschl\"ussel (2024) arXiv:2404.06205 to improve finite sample properties and extend their applicability to a generalised framework, allowing for non-stationary volatility. Numerical evidence shows the bootstrap to improve the tests' precision for error processes that promote spurious rejections of the unit root null, depending on the detrending procedure. The bootstrap mitigates finite-sample size distortions and restores asymptotically valid inference when the data features time-varying unconditional variance. We apply the bootstrap tests to real residential property prices of the top six Eurozone economies and find evidence of stationarity to be period-specific, supporting the conjecture that exuberance in the housing market characterises the development of Euro-era residential property prices in the recent past.