On a double-threshold autoregressive heteroscedastic time series model
扩展了Tong的门限模型，提出双门限ARCH模型，可同时处理条件均值和条件方差的分段线性特征，适用于金融数据中涨跌市场的不对称行为分析，并给出了模型识别、估计和诊断检验方法。
Tong's threshold models have been found useful in modelling nonlinearities in the conditional mean of a time series. The threshold model is extended to the so-called double-threshold ARCH(DTARCH) model, which can handle the situation where both the conditional mean and the conditional variance specifications are piecewise linear given previous information. Potential applications of such models include financial data with different (asymmetric) behaviour in a rising versus a falling market and business cycle modelling. Model identification, estimation and diagnostic checking techniques are developed. Maximum likelihood estimation can be achieved via an easy-to-use iteratively weighted least squares algorithm. Portmanteau-type statistics are also derived for checking model adequacy. An illustrative example demonstrates that asymmetric behaviour in the mean and the variance could be present in financial series and that the DTARCH model is capable of capturing these phenomena.