A Study on Locally Persistent Time Series

Abstract

While it is recognized that many economic time series are highly persistent over certain ranges, less persistent results are also found around very long horizons, indicating the existence of local or temporary persistency. Seeking to describe the dynamics of locally persistent processes, this thesis uses a block local-to-unity model. A test for stationarity against locally persistency is studied. An empirical application using US time series of real GNP, real interest rates and real exchange rates illustrates the importance of this class of processes and tests for applied works. It is also studied co-movement of time series with local persistency. In particular, a residual based test for the null hypothesis of co-movement between two processes with local persistency is proposed. With this new technique, one fills in an existing lacuna in econometrics, in which long-run relationships can also be studied if the dependent and independent variables do not have a unit root, but do exhibit local persistency. The thesis is finalized by applying the proposed test to study the Fisher effect in the determination of real interest rate.