Nonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of theresearch has concentrated on the empirical applications of various models, with little...

In this paper, we introduce a linearity test for fuzzy rule-based models in the framework of time series modeling. To do so, we explore a family of statistical models, the regime switching autoregressive models, and the relations that link them to the fuzzy rule-based models. From these...

We study the simultaneous occurrence of long memory and nonlinear effects, such as structural breaks and thresholds, in autoregressive moving average (ARMA) time series models and apply our modeling framework to series of daily realized volatility. Asymptotic theory for the quasi-maximum...