add.local.level {bsts}

Local level trend state component

Description

Add a local level model to a state specification. The local level model assumes the trend is a random walk:

\alpha_{t+1} = \alpha_t + \epsilon_t \qquad \epsilon_t \sim \mathcal{N}(0,\sigma).

The prior is on the \sigma parameter.

Usage

  AddLocalLevel(
     state.specification,
     y,
     sigma.prior,
     initial.state.prior,
     sdy,
     initial.y)

Arguments

state.specification

A list of state components that you wish to add to. If omitted, an empty list will be assumed.

y

The time series to be modeled, as a numeric vector.

sigma.prior

An object created by SdPrior describing the prior distribution for the standard deviation of the random walk increments.

initial.state.prior

An object created using NormalPrior, describing the prior distribution of the initial state vector (at time 1).

sdy

The standard deviation of the series to be modeled. This will be ignored if y is provided, or if all the required prior distributions are supplied directly.

initial.y

The initial value of the series being modeled. This will be ignored if y is provided, or if the priors for the initial state are all provided directly.

Value

Returns a list with the elements necessary to specify a local linear trend state model.

Author(s)

Steven L. Scott [e-mail]

References

Harvey (1990), "Forecasting, structural time series, and the Kalman filter", Cambridge University Press.

Durbin and Koopman (2001), "Time series analysis by state space methods", Oxford University Press.

See Also

bsts. SdPrior NormalPrior