MINIMUM DISTANCE ESTIMATION OF NONSTATIONARY TIME SERIES MODELS
研究了非平稳时间序列模型中最小距离估计量的极限分布，推导了更易验证的正则条件，并提出了最优权重矩阵和拟合优度检验，适用于永久收入模型和现值模型。
This paper analyzes the limit distribution of minimum distance (MD) estimators for nonstationary time series models that involve nonlinear parameter restrictions. A rotation for the restricted parameter space is constructed to separate the components of the MD estimator that converge at different rates. We derive regularity conditions for the restriction function that are easier to verify than the stochastic equicontinuity conditions that arise from direct estimation of the restricted parameters. The sequence of matrices that is used to weigh the discrepancy between the unrestricted estimates and the restriction function is allowed to have a stochastic limit. For MD estimators based on unrestricted estimators with a mixed normal asymptotic distribution the optimal weight matrix is derived and a goodness-of-fit test is proposed. Our estimation theory is illustrated in the context of a permanent-income model and a present-value model.