tsmoments.tsissm.estimate {tsissm} | R Documentation |
Analytic Forecast Moments
Description
Prediction function for class “tsissm.estimate”.
Usage
## S3 method for class 'tsissm.estimate'
tsmoments(
object,
h = 1,
newxreg = NULL,
init_states = NULL,
transform = FALSE,
...
)
Arguments
object |
an object of class “tsissm.estimate”. |
h |
the forecast horizon. |
newxreg |
a matrix of external regressors in the forecast horizon. |
init_states |
optional vector of states to initialize the forecast. If NULL, will use the last available state from the estimated model. |
transform |
whether to back transform the mean forecast. For the Box-Cox transformation this uses a Taylor Series expansion to adjust for the bias. |
... |
not currently used. |
Details
For the constant variance model the conditional moments are given by:
E\left(y_{n+h|n}^{(\omega)}\right) = \mathbf{w}' \mathbf{F}^{h-1}\mathbf{x}_n
V\left(y_{n+h|n}^{(\omega)}\right) =
\begin{cases}
\sigma^2, & \text{if } h = 1, \\[6pt]
\sigma^2 \left[1 + \sum_{j=1}^{h-1} c_j^2 \right], & \text{if } h \geq 2.
\end{cases}
The backtransformed variance should be used with caution as it uses a higher-order expansion correction which is known to be inaccurate for h > 5. Instead, use the simulated distribution to extract this information.
Value
a list with a slot for the analytic mean and one for the process variance. In the case of dynamic variance, it returns an additional slot for the GARCH variance.