add.local.linear.trend {bsts} R Documentation

## Local linear trend state component

### Description

Add a local linear trend model to a state specification. The local linear trend model assumes that both the mean and the slope of the trend follow random walks. The equation for the mean is

mu[t+1] = mu[t] + delta[t] + rnorm(1, 0, sigma.level).

The equation for the slope is

delta[t+1] = delta[t] + rnorm(1, 0, sigma.slope).

The prior distribution is on the level standard deviation sigma.level and the slope standard deviation sigma.slope.

### Usage

```  AddLocalLinearTrend(
state.specification = NULL,
y,
level.sigma.prior = NULL,
slope.sigma.prior = NULL,
initial.level.prior = NULL,
initial.slope.prior = NULL,
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. `level.sigma.prior` An object created by `SdPrior` describing the prior distribution for the standard deviation of the level component. `slope.sigma.prior` An object created by `SdPrior` describing the prior distribution of the standard deviation of the slope component. `initial.level.prior` An object created by `NormalPrior` describing the initial distribution of the level portion of the initial state vector. `initial.slope.prior` An object created by `NormalPrior` describing the prior distribution for the slope portion of the initial state vector. `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 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`

### Examples

```  data(AirPassengers)
y <- log(AirPassengers)
ss <- AddLocalLinearTrend(list(), y)
ss <- AddSeasonal(ss, y, nseasons = 12)
model <- bsts(y, state.specification = ss, niter = 500)
pred <- predict(model, horizon = 12, burn = 100)
plot(pred)
```

[Package bsts version 0.9.6 Index]