ARCH and Bilinear Time Series Models: Comparison and Combination
比较了ARMA模型的两种扩展：双线性和ARCH误差，并探讨了它们的结合，讨论了参数估计和模型检验方法，指出为正确区分两者需结合成带ARCH误差的双线性模型，并应用于两个实际时间序列。
Two extensions to the ARMA model, bilinearity and ARCH errors are compared, and their combination is considered. Starting with the ARMA model, tests for each extension are discussed, along with various least squares and maximum likelihood estimates of the parameters and tests of the estimated models based on these. The effects each may have on the identification, estimation, and testing of the other are given, and it is seen that to distinguish between the two properly, it is necessary to combine them into a bilinear model with ARCH errors. Some consequences of the misspecification caused by considering only the ARMA model are noted, and the methods are applied to two real time series.