Testing for Parameter Instability and Structural Change in Persistent Predictive Regressions

This paper proposes a consistent inference procedure for predictive regressions in economic systems governed by fractionally integrated vector autoregressive dynamics that may be subject to low-frequency contamination such as structural, or Markov-switching, breaks, outliers and deterministic trends. Specifically, we modify the local spectrum (LCM) inference procedure (Andersen & Varneskov (2019)), making it robust towards such features by establishing new results for the first-stage filtering as well as the second-stage trimming. The modified LCM estimator and tests are asymptotically normal and chi^2, respectively, despite the variables having different integration orders and being low-frequency contaminated. As bi-products of our analysis, we provide a modified exact local Whittle estimator of the integration order and a modified test for cointegration rank, which are both robust to contamination. Furthermore, we provide consistent estimators of the coherence between (unknown) low-frequency contaminants. The validity of the estimators and tests are examined in a simulation study. Finally, we use the new framework to dissect the dynamic properties and dependencies in popular first-order VAR systems in macro finance.