Do shocks last forever? Local persistency in economic time series

While it is recognized that many macroeconomic time series are highly persistent over certain range, less persistent results are also found around very long horizons, indicating the existence of local or temporary persistency. In this paper, we study locally persistent behavior in economic time series. A test for stationarity against locally persistent alternative is proposed. Asymptotic analysis of the test statistic are provided under both the null and the alternative hypothesis of local persistency. Monte Carlo experiment is conducted to study the power and size of the test. An empirical application reveals that many US economic variables may exhibit local persistency.