Threshold Autoregression, Limit Cycles and Cyclical Data

作者：Hưng Tâm Tống, K. S. Lim · 发表于：Journal of the Royal Statistical Society Series B (Statistical Methodology) · 年份：1980 · DOI：10.1111/j.2517-6161.1980.tb01126.x · 被引用次数：1327 · 研究领域：Complex Systems and Time Series Analysis、Financial Risk and Volatility Modeling、Chaos control and synchronization

Summary The notion of a limit cycle, which can only exist in a non-linear system, plays the key role in the modelling of cyclical data. We have shown that the class of threshold autoregressive models is general enough to capture this notion, a definition of which in discrete time is proposed. The threshold value has an interesting interpretation. Simulation results are presented which demonstrate that this new class of models exhibits some well-known features of non-linear vibrations. Detailed analyses of several real data sets are discussed.