ARMA Memory Index Modeling of Economic Time Series
证明，对于取有理数值的经济时间序列，可以用一个自回归移动平均随机变量来捕捉其全部历史信息，从而将回归模型表示为过去观测的非线性函数，并应用于非线性ARX模型的设定检验。
In this paper, it will be shown that if we condition a k -variate rational-valued time series process on its entire past, it is possible to capture all relevant information on the past of the process by a single random variable. This scalar random variable can be formed as an autoregressive moving average of past observations; Since economic data are usually reported in a finite number of digits, this result applies to virtually all economic time series. Therefore, economic time series regressions generally take the form of a nonlinear function of an autoregressive moving average of past observations. This approach is applied to model specification testing of nonlinear ARX models.