add.shared.local.level: Local level trend state component

In bsts: Bayesian Structural Time Series

Local level trend state component

Description

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

\alpha_{t+1} = \alpha_t + \eta_t \qquad \eta_{tj} \sim \mathcal{N}(0,\sigma_j).

The contribution to the mean of the observed series obeys

y_{t} = B \alpha_t + \epsilon_t.

plus observation error. Identifiability constraints imply that the observation coefficients B form a rectangular lower triangular matrix with diagonal 1.0.

If there are m time series and p factors, then B has m rows and p columns. Having B be lower triangular means that the first factor affects all series. The second affects all but the first, the third excludes the first two, etc.

Usage

  AddSharedLocalLevel(
     state.specification,
     response,
     nfactors,
     coefficient.prior = NULL,
     initial.state.prior = NULL,
     timestamps = NULL,
     series.id = NULL,
     sdy,
     ...)

Arguments

state.specification	A pre-existing list of state components that you wish to add to. If omitted, an empty list will be assumed.
response	The time series to be modeled. This can either be a matrix with rows as time and columns as series, or it can be a numeric vector. If a vector is passed then timestamps and series.id are required. Otherwise they are unused.
nfactors	The number of latent factors to include in the model. This is the dimension of the state for this model component.
coefficient.prior	Prior distribution on the observation coefficients.
initial.state.prior	An object of class MvnPrior, describing the prior distribution of the initial state vector (at time 1).
timestamps	If response is in long format (i.e. a vector instead of a matrix) this argument is a vector of the same length indicating the time index to which each element of response belongs.
series.id	If response is in long format (i.e. a vector instead of a matrix) this argument is a vector of the same length indicating the time series to which each element of response belongs.
sdy	A vector giving the standard deviation of each series to be modeled. This argument is only necessary if response cannot be supplied directly.
...	Extra arguments passed to ConditionalZellnerPrior, used to create a default prior for the observation coefficients when coefficient.prior is left as NULL.

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

bsts documentation built on Sept. 9, 2025, 5:27 p.m.