Local linear trend state block

Local linear trend state block

Usage

locallineartrend(
  name,
  levelVariance = 0.01,
  slopeVariance = 0.01,
  fixedLevelVariance = FALSE,
  fixedSlopeVariance = FALSE
)

Arguments

name

Name of the block

levelVariance

variance of the level (\(\sigma^2_l\))

fixedLevelVariance, fixedSlopeVariance

boolean that triggers the estimation of the variances \(\sigma^2_l\) and \(\sigma^2_n\) (FALSE) or fixes it (TRUE) to a pre-specified value set by the parameters levelVariance and slopevariance.

Details

$$\begin{cases}l_{t+1} = l_t + n_t + \xi_t \\ n_{t+1} = n_t + \mu_t \\ \xi_t \sim N(0, \sigma^2_l)\\ \mu_t \sim N(0, \sigma^2_n) \end{cases}$$

Examples

llt<-locallineartrend('llt', levelVariance=1, slopeVariance=.25)
print(block_t(llt))
#>      [,1] [,2]
#> [1,]    1    1
#> [2,]    0    1