Matlab 对向量时间序列的 VAR[X] 系数约束
Matlab's VAR[X] coefficient constraints for vector time series
Matlab 的 VARMAX 模型允许用户设置标志，以确定是否要估计各个线性系数。特别是，vgxset 接受一个 ARsolve 参数，该参数包含确定是否估计各个时间序列滞后系数的标志。每个标量滞后项都有单独的标量标志这一事实意味着每个系数都可以独立激活。
我有 3 个关于此灵活功能的问题。
(1)关闭一个flag本质上是否意味着对应的系数为零？
(2)哪个开关对应哪个系数的文档在哪里？也就是说，对于给定的滞后，如果我想打开系列 i 对系列 j 的依赖系数，我会打开标志 (i,j) 还是 (j,i)？
(3)既然AR0solve被忽略了，是不是意味着时间序列之间没有同期相关性？
我已将此发布到：
2015 年 5 月 29 日星期五 UTC-4 2:05:06 下午，Rick 写道：
(1) No, not necessarily. Turning off a flag (i.e., setting a
particular element of an input "solve" flag to logical FALSE) holds
the corresponding parameter value fixed throughout the estimation.
For example, if, say, the 3rd element of the "asolve" parameter is
FALSE (logical 0) and the 3rd element of the corresponding value
parameter "a" is such that a(3) = 0, then the estimation will
effectively exclude that coefficient from the model.
The important thing is that the parameter is held fixed at whatever
you specify. Of course, to hold a coefficient fixed you also need to
indicate the its value, and so the "asolve" and "a" parameters must
both be set.
These values do not necessarily need to be zero, although zeros
(i.e., exclusion constraints) are very common.
(2) The best I have found is the reference page for "vgxset"
function. There might be specific examples in the documentation, but
the reference page is the place I'd start.
As for your 2nd sentence, I think you are over-thinking the storage.
There is a 1-to1 correspondence between the solve parameter and its
paired value.
I suggest you simply write out a 2-D VAR model and contrive a
simple experiment. The model, and placement of coefficients and
corresponding TRUEs/FALSEs, conforms to the linear algebra of the
equation.
(3) Yes, at least from the perspective of model estimation.
That is, "vgxvarx" will not estimate "structural" VAR models, and so
the corresponding "AR0" structural coefficient is not estimated. You
can specify a non-identity AR0 coefficient, in which case the
estimation simply fits the VAR model to the modified series A0*y(t).
So, in this case you can effect contemporaneous dependence between
the series, but you cannot estimate it.
2015 年 5 月 29 日星期五 2:40:28 下午 UTC-4，paul.d...@gmail.com
写道：
I just want to check a specific detail about answer#2. I am
thinking of the matrix representation of the equations when I mull
over the vgxset parameters. Are the boolean flags for solving the
coefficients suppose to form a symmetric matrix? I was more
interested in the assymetric case were, e.g., for a given lag,
series i depends on series j according to some coefficient that is
different from the dependence of series j on series i. If that
constraint is not necessary, and the flags occupy exactly the same
positions as the coefficients themselves, I think I can run with
that.
2015 年 5 月 30 日星期六 6:41:04 上午 UTC-4，Rick 写道：
Paul, no, the Boolean flags need not form a symmetric matrix. Best, Rick
所以得到flag的行和列的含义就变得很重要，而行和列的含义来自于flag对应的系数矩阵。根据我对矢量设置的理解，行代表相关序列，而列代表预测序列。
Matlab 的 VARMAX 模型允许用户设置标志，以确定是否要估计各个线性系数。特别是，vgxset 接受一个 ARsolve 参数，该参数包含确定是否估计各个时间序列滞后系数的标志。每个标量滞后项都有单独的标量标志这一事实意味着每个系数都可以独立激活。
我有 3 个关于此灵活功能的问题。
(1)关闭一个flag本质上是否意味着对应的系数为零？
(2)哪个开关对应哪个系数的文档在哪里？也就是说，对于给定的滞后，如果我想打开系列 i 对系列 j 的依赖系数，我会打开标志 (i,j) 还是 (j,i)？
(3)既然AR0solve被忽略了，是不是意味着时间序列之间没有同期相关性？
我已将此发布到：
2015 年 5 月 29 日星期五 UTC-4 2:05:06 下午，Rick 写道：
(1) No, not necessarily. Turning off a flag (i.e., setting a particular element of an input "solve" flag to logical FALSE) holds the corresponding parameter value fixed throughout the estimation.
For example, if, say, the 3rd element of the "asolve" parameter is FALSE (logical 0) and the 3rd element of the corresponding value parameter "a" is such that a(3) = 0, then the estimation will effectively exclude that coefficient from the model.
The important thing is that the parameter is held fixed at whatever you specify. Of course, to hold a coefficient fixed you also need to indicate the its value, and so the "asolve" and "a" parameters must both be set.
These values do not necessarily need to be zero, although zeros (i.e., exclusion constraints) are very common.
(2) The best I have found is the reference page for "vgxset" function. There might be specific examples in the documentation, but the reference page is the place I'd start.
As for your 2nd sentence, I think you are over-thinking the storage. There is a 1-to1 correspondence between the solve parameter and its paired value.
I suggest you simply write out a 2-D VAR model and contrive a simple experiment. The model, and placement of coefficients and corresponding TRUEs/FALSEs, conforms to the linear algebra of the equation.
(3) Yes, at least from the perspective of model estimation.
That is, "vgxvarx" will not estimate "structural" VAR models, and so the corresponding "AR0" structural coefficient is not estimated. You can specify a non-identity AR0 coefficient, in which case the estimation simply fits the VAR model to the modified series A0*y(t). So, in this case you can effect contemporaneous dependence between the series, but you cannot estimate it.
2015 年 5 月 29 日星期五 2:40:28 下午 UTC-4，paul.d...@gmail.com 写道：
I just want to check a specific detail about answer#2. I am thinking of the matrix representation of the equations when I mull over the vgxset parameters. Are the boolean flags for solving the coefficients suppose to form a symmetric matrix? I was more interested in the assymetric case were, e.g., for a given lag, series i depends on series j according to some coefficient that is different from the dependence of series j on series i. If that constraint is not necessary, and the flags occupy exactly the same positions as the coefficients themselves, I think I can run with that.
2015 年 5 月 30 日星期六 6:41:04 上午 UTC-4，Rick 写道：
Paul, no, the Boolean flags need not form a symmetric matrix. Best, Rick
所以得到flag的行和列的含义就变得很重要，而行和列的含义来自于flag对应的系数矩阵。根据我对矢量设置的理解，行代表相关序列，而列代表预测序列。