Long memory and regime switching

The theoretical and empirical econometric literatures on long memory and regime switching have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related, and we substantiate our claim in several environments, including a simple mixture model, Engle and Smithʹs (Rev. Econom. Statist. 81 (1999) 553–574) stochastic permanent break model, and Hamiltonʹs (Econometrica 57 (1989) 357–384) Markov-switching model. In particular, we show analytically that stochastic regime switching is easily confused with long memory, even asymptotically, so long as only a “small” amount of regime switching occurs, in a sense that we make precise. A Monte Carlo analysis supports the relevance of the theory and produces additional insights.