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Statistica Sinica 30 (2020), 809-827

CONDITIONAL QUANTILE ESTIMATION FOR
HYSTERETIC AUTOREGRESSIVE MODELS
Degao Li1 , Ruochen Zeng2 , Liwen Zhang3 , Wai Keung Li2 and Guodong Li2
1Jiaxing University, 2University of Hong Kong,
and 3Shanghai University of Finance and Economics

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.

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