tsmoments: Analytic Forecast Moments

In tsissm: Linear Innovations State Space Unobserved Components Model

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.

tsissm documentation built on Aug. 8, 2025, 6:08 p.m.