Limiting distributions of unconditional maximum likelihood unit root test statistics in seasonal time–series models
研究了季节性时间序列模型中基于无条件最大似然估计的单位根检验统计量的极限分布，扩展了Gonzalez-Farias的非季节性方法，适用于含均值或趋势的模型。
Abstract. The likelihood function of a seasonal model, Y t = ρ Y t − d + e t as implemented in computer algorithms under the assumption of stationary initial conditions is a function of ρ which is zero at the point ρ = 1. It is a smooth function for ρ in the above seasonal model with a well‐defined maximum regardless of the data‐generating mechanism. Gonzalez‐Farias (PhD Thesis, North Carolina State University, 1992) proposed tests for unit roots based on maximizing the stationary likelihood function in nonseasonal time series. We extend it to seasonal time series. The limiting distribution of seasonal unit root test statistics based on the unconditional maximum likelihood estimators are shown. Models having a single mean, seasonal means, and a single‐trend variable across the seasons are considered.