无约束自回归过程平稳性的理论分析
A Theoretical Analysis of the Stationarity of an Unrestricted Autoregression Process
摘要：
高维自回归模型如果考虑到时间依赖的异质性，则可以较一般地描述某些计量经济过程。本文分析了具有系数序列$β$乘以$0<δ<1$的连续递增幂的维数$k>1$的自回归过程的平稳性。该定理给出了系数与$k$之间按$δ$的简单关系的平稳性条件。在计算上，平稳性的证据取决于参数。$δ$的选择设定了$β$的界限和模型预测的时滞数。
英文摘要：
The higher dimensional autoregressive models would describe some of the econometric processes relatively generically if they incorporate the heterogeneity in dependence on times. This paper analyzes the stationarity of an autoregressive process of dimension $k>1$ having a sequence of coefficients $β$ multiplied by successively increasing powers of $0<δ<1$. The theorem gives the conditions of stationarity in simple relations between the coefficients and $k$ in terms of $δ$. Computationally, the evidence of stationarity depends on the parameters. The choice of $δ$ sets the bounds on $β$ and the number of time lags for prediction of the model.
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