R: Local level trend state component

add.shared.local.level {bsts}

R Documentation

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 steve.the.bayesian@gmail.com

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.