Unit roots in lower-bounded series with outliers

Abstract

This study examines a unit root process in lower-bounded time series with additive outliers. A standard unbounded unit root test may be unsuitable when applied to nonnegative or lower-bounded data; therefore, lower-bounded unit root tests that handle outliers are proposed. The results demonstrate that these tests reject less frequently the null hypothesis of unit root because of a nuisance parameter associated with the lower bound, either in homoskedastic or heteroskedastic settings. The empirical study of inflation and stock market volatility in South America reveals the presence of outliers related to the hyperinflation crisis and stock markets owing to multiple shocks, such as the recent COVID-19 pandemic. Moreover, these series cannot reject the unit root hypothesis if the lower bound is considered.