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, ] + rnorm(nfactors, 0, sigma).

The contribution to the mean of the observed series obeys

y[t, ] = B %*% alpha[t, ]

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

### 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. This currently must be a `ScaledMatrixNormalPrior`. Expect other choices in the future.
`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.

### See Also

`bsts`. `SdPrior` `NormalPrior`

[Package bsts version 0.9.6 Index]