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Generalized Local-To-Unity Models, Liyu Dou, Ulrich K. Müller

Research Collection School Of Economics

We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and …