Long memory and regime switching

The theoretical and empirical econometric literatures on long memory and re gime switching have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related, and we s ubstantiate our claim in several environments, including a simple mixture m odel, Engle and Smith's (Rev. Econom. Statist. 81 (1999) 553-574) stochasti c permanent break model, and Hamilton's (Econometrica 57 (1989) 357-384) Ma rkov-switching model. In particular, we show analytically that stochastic r egime switching is easily confused with long memory, even asymptotically, s o 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 theo ry and produces additional insights. (C) 2001 Elsevier Science S.A. All rig hts reserved.