add.shared.local.level: 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,
     ...)

Value

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

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.

Author

Steven L. Scott steve.the.bayesian@gmail.com

References

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