在 ARIMA 或 VAR 模型中选择特定的滞后 [英] Choosing specific lags in ARIMA or VAR Model

问题描述

我已经看到这个问题提出 这里和here 但不幸的是，答案并不令人满意.在 VAR 中的 p 参数或 arima 中的 order 参数中输入滞后，R 将包括所有滞后于或低于该规定值.

I've seen this issue raised here and here but unfortunately the answers are not satisfactory. Inputting the lags in either the p argument in VAR or the order argument in arima, R will include all the lags at and below that stated value.

但是，如果您只想要特定的延迟怎么办?例如，如果我只想在 VAR 中使用滞后 1、2 和 4 怎么办?在 VAR 中输入 P=4 会给我滞后 1、2、3 和 4，但我想排除第三个滞后.

However, what if you want specific lags only? For example, what if I wanted lags 1, 2, and 4 only in a VAR? Inputting P=4 in VAR will give me lags 1,2,3 and 4, but I would like to exclude the third lag.

在第一个链接中，用户通过说明他可以使用季节性参数来包含滞后 1,2 和 4 来提供答案，因为他的数据是季度的，但这仅适用于特殊情况，不是通用解决方案.

In the first link, the user provided an answer by stating he can use the seasonal parameter to include lags 1,2 and 4 since his data is quarterly, however that is only for a special case and is not a general solution.

推荐答案

幸运的是，我们可以轻松地为这两个模型做到这一点.例如，在 ARIMA(3,0,3) 的情况下，这里是如何降低第二个 AR 滞后和第一个 MA 滞后:

Fortunately, we can easily do this for both models. For example, in case of ARIMA(3,0,3) here is how to drop the second AR lag and the first MA lag:

arima(lh, order = c(3, 0, 3), fixed = c(NA, 0, NA, 0, NA, NA, NA))

Call:
arima(x = lh, order = c(3, 0, 3), fixed = c(NA, 0, NA, 0, NA, NA, NA))

Coefficients:
         ar1  ar2      ar3  ma1      ma2      ma3  intercept
      0.6687    0  -0.1749    0  -0.0922  -0.1459     2.3909
s.e.  0.1411    0   0.1784    0   0.1788   0.2415     0.0929

sigma^2 estimated as 0.1773:  log likelihood = -26.93,  aic = 65.87
Warning message:
In arima(lh, order = c(3, 0, 3), fixed = c(NA, 0, NA, 0, NA, NA,  :
  some AR parameters were fixed: setting transform.pars = FALSE

这里的 fixed 是一个与参数总数长度相同的可选数字向量.如果提供，则只有固定中的 NA 条目会发生变化"；有关警告等的更多详细信息，请参见 ?arima.fixed 的每个元素对应于显示的系数向量(或 coef(arima(...)))，例如fixed[3]对应ar3，fixed[7]对应intercept.

Here fixed is an "optional numeric vector of the same length as the total number of parameters. If supplied, only NA entries in fixed will be varied"; see ?arima for more details about the warning, etc. Each element of fixed corresponds to the respective element from the displayed vector of coefficients (or coef(arima(...))), e.g. fixed[3] corresponds to ar3 and fixed[7] to intercept.

同样，vars 中的 restrict 是 VAR 模型所需要的.同样，您必须指定您的限制，这次是在矩阵 resmat 中，例如让我们使用 VAR(2) 并删除 e 的第二个滞后和 prod 的第一个滞后:

Similarly, restrict from vars is what you need for VAR models. Again, you have to specify yours restrictions, this time in the matrix resmat, e.g. let us take VAR(2) and drop the second lag of e and the first of prod:

data(Canada)
model <- VAR(Canada[, 1:2], p = 2, type = "const")
restrict <- matrix(c(1, 0, 0, 1, 1, 
                     1, 0, 0, 1, 1),
                   nrow = 2, ncol = 5, byrow = TRUE)
coef(restrict(model, method = "man", resmat = restrict))
$e
          Estimate Std. Error   t value     Pr(>|t|)
e.l1     0.9549881 0.01389252 68.741154 3.068870e-72
prod.l2  0.1272821 0.03118432  4.081607 1.062318e-04
const   -8.9867864 6.46303483 -1.390490 1.682850e-01

$prod
            Estimate  Std. Error   t value     Pr(>|t|)
e.l1      0.04130273  0.02983449  1.384396 1.701355e-01
prod.l2   0.94684968  0.06696899 14.138628 2.415345e-23
const   -17.02778014 13.87950374 -1.226829 2.235306e-01

resmat 的第一行对应第一个方程，所有系数都和无限制模型中的一样:e.l1, prod.l1, e.l2, prod.l2, const，即 restrict[1, 5] 对应于截距，同样适用于第二个矩阵行.

The first row of resmat corresponds to the first equation and all the coefficients go just as in the unrestricted model: e.l1, prod.l1, e.l2, prod.l2, const, i.e. restrict[1, 5] corresponds to the intercept and the same holds for the second matrix row.

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