Threshold Autoregressions for Strongly Autocorrelated Time Series

In some cases the unit root or near unit root behavior of linear autoregressive models fitted to economic time series is not in accordance with the underlying economic theory. To accommodate this feature we consider a threshold autoregressive (TAR) process with the threshold effect only in the intercept term. Although these processes are stationary, their realizations switch between different regimes and can therefore closely resemble those of (near) integrated processes for sample sizes relevant in many economic applications. Estimation and inference of these TAR models are discussed, and a specification test for testing their stability is derived. Testing is based on the idea that if (near) integratedness is really caused by level shifts, the series purged of these shifts should be stable so that known stationarity tests can be applied to this series. Simulation results indicate that in certain cases these tests, like several linearity tests, can have low power. The proposed model is applied to interest rate data.

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