Margin‐closed vector autoregressive time series models
研究了高斯向量自回归模型在何种条件下其单变量或低维边际序列仍保持自回归结构，提出一种边际封闭模型，允许先拟合子过程再组装，并用宏观经济数据验证了效果。
Conditions are obtained for a Gaussian vector autoregressive time series of order , VAR(), to have univariate margins that are autoregressive of order or lower‐dimensional margins that are also VAR(). This can lead to ‐dimensional VAR() models that are closed with respect to a given partition of by specifying marginal serial dependence and some cross‐sectional dependence parameters. The special closure property allows one to fit the subprocesses of multi‐variate time series before assembling them by fitting the dependence structure between the subprocesses. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR() process with non‐Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher‐dimensional time series and a multi‐stage estimation procedure can be used. The proposed class of models is applied to a macro‐economic data set and compared with the relevant benchmark models.