Conditions are obtained for a Gaussian vector autoregressive time series of order $k$, VAR($k$), to have univariate margins that are autoregressive of order $k$ or lower-dimensional margins that are also VAR($k$). This can lead to $d$-dimensional VAR($k$) models that are closed with respect to a given partition $\{S_1,\ldots,S_n\}$ of $\{1,\ldots,d\}$ by specifying marginal serial dependence and some cross-sectional dependence parameters. The special closure property allows one to fit the sub-processes of multivariate time series before assembling them by fitting the dependence structure between the sub-processes. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR($k$) 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.
翻译:Gausian 矢量自动递增时间序列要求为 $1,\\\ldots, VAR(k$), 以自动递减为 $1, VAR(k$) 的单亚值边距, 以自动递减为 $1, VAR(k$) 或 VAR(k$) 的低维边距为 瓦尔(k$), 其条件可以是 $1, 1,\\ldots, S_n $1, 美元, d_ 美元, 通过指定边际序列依赖和某些跨部门依赖参数, 以获得条件。 特殊封闭属性允许在匹配多变量时间序列的子进程之前, 将这些子进程匹配成一个子进程, 美元或低维维维值边距也是 VAR(k$美元) 。 这可能导致在 VAR(k$) 进程固定联合发布观测结果时使用 Gaussisian univariate perate press, 但受边际关闭制约的情况下, 。 这种构造允许在处理较高时间序列和多阶段时间序列和多阶段估算程序方面有更大的灵活性。 。 。 。, 可使用拟议的模型与相关的基准用于与相关的基准, 。