Prediction function for class “tsissm.estimate”.
# S3 method for tsissm.estimate
tsmoments(
object,
h = 1,
newxreg = NULL,
init_states = NULL,
transform = FALSE,
...
)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.
an object of class “tsissm.estimate”.
the forecast horizon.
a matrix of external regressors in the forecast horizon.
optional vector of states to initialize the forecast. If NULL, will use the last available state from the estimated model.
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.
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.