Threshold autoregression in economics

Abstract

The threshold autoregressive (TAR) model developed by Howell Tong has been enormously influential in economics. A simple illustration of the depth of this influence is to examine the recent edition of the graduate text Applied Econometric Time Series by Walter Enders [25] and observe that 60 pages of the text are devoted to nonlinear time series models, with the bulk devoted to TAR models. My goal in this paper is to document the influence of Howell Tong’s TAR model in the fields of econometrics and economics. I do so by reviewing 75 papers published in the econometrics and economics literatures which either contribute to the theory of TAR estimation and inference, or report a substantive application of a TAR model to economics. Many of these papers are themselves highly cited. This literature is enormous, and the papers reviewed here are not an exhaustive list of all applications of the TAR model. I focus on the more substantial and influential papers. Closely related to the TAR model is the smoothtransition autoregressive (STAR) model which has been equally influential in economics. To keep the attention focused, I do not review this literature here. Extensive reviews on the STAR model in economics can be found in the monographs by Granger and Terasvirta [38] and Franses and van Dijk [31], and the review paper by van Dijk, Terasvirta and Franses [23]. In Section 2 I review the literature on the econometric theory of TAR estimation and inference. In Section 3 I review empirical applications of the TAR model.