Adaptive LAD-Based Bootstrap Unit Root Tests under Unconditional Heteroskedasticity

TL;DR

This paper develops adaptive LAD-based bootstrap unit root tests that effectively handle unconditional heteroskedasticity and serial dependence, improving size control and power over traditional tests, with applications to real exchange rate data.

Contribution

The paper introduces a novel adaptive block bootstrap method for LAD-based unit root testing under heteroskedasticity and serial dependence, extending the applicability of LAD tests.

Findings

Bootstrap tests control size well under heteroskedasticity.

Proposed tests outperform benchmarks in heavy-tailed cases.

Empirical analysis demonstrates practical applicability.

Abstract

This paper explores testing unit roots based on least absolute deviations (LAD) regression under unconditional heteroskedasticity. We first derive the asymptotic properties of the LAD estimator for a first-order autoregressive process with the coefficient (local to) unity under unconditional heteroskedasticity and weak dependence, revealing that the limiting distribution of the LAD estimator (consequently the derived test statistics) is closely associated with unknown time-varying variances. To conduct feasible LAD-based unit root tests under heteroskedasticity and serial dependence, we develop an adaptive block bootstrap procedure, which accommodates time-varying volatility and serial dependence, both of unknown forms, to compute critical values for LAD-based tests. The asymptotic validity is established. We then extend the testing procedure to allow for deterministic components. Simulation results indicate that, in the presence of unconditional heteroskedasticity and serial dependence, the classic LAD-based tests demonstrate severe size distortion, whereas the proposed LAD-based bootstrap tests exhibit good size-control capability. Additionally, the newly developed tests show superior testing power in heavy-tailed distributed cases compared to considered benchmarks. Finally, empirical analysis of real effective exchange rates of 16 EU countries is conducted to illustrate the applicability of the newly proposed tests.