Abstract: The phenomenon of hysteresis has been observed in many economic time series, especially in unemployment rates. To study the hysteretic patterns at different quantiles, this study considers a conditional quantile estimation for hysteretic autoregressive models, and derives its asymptotic properties. Simulation experiments are conducted to evaluate the finite-sample performance of our method, and its usefulness is further demonstrated by an analysis of the growth rates of unemployment rates.

Key words and phrases: Autoregression, conditional quantile estimation, hysteretic model, threshold model.