On the Noninvertible Moving Average Time Series with Infinite Variance
研究了具有无限方差新息的不可逆和近似不可逆移动平均模型的最小二乘估计的极限分布，该分布是Lévy过程的泛函，可用于检验单位根和过度差分。
The limiting distribution of the least squares estimate of the derived process of a noninvertible and nearly noninvertible moving average model with infinite variance innovations is established as a functional of a Lévy process. The form of the limiting law depends on the initial value of the innovation and the stable index α. This result enables one to perform asymptotic testing for the presence of a unit root for a noninvertible moving average model through the constructed derived process under the null hypothesis. It provides not only a parallel analog of its autoregressive counterparts, but also a useful alternative to determine “over-differencing” for time series that exhibit heavy-tailed phenomena.