add.seasonal: Seasonal State Component
In michelletran/bsts: Bayesian Structural Time Series

Description Usage Arguments Value Author(s) References See Also Examples

Add a seasonal model to a state specification.

The seasonal model can be thought of as a regression on nseasons dummy variables with coefficients constrained to sum to 1 (in expectation). If there are S seasons then the state vector gamma is of dimension S-1. The first element of the state vector obeys

gamma[t+1, 1] = -1 * sum(gamma[t, -1]) + rnorm(1, 0, sigma)

  AddSeasonal(
     state.specification,
     y,
     nseasons,
     season.duration = 1,
     sigma.prior,
     initial.state.prior,
     sdy)

`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.
`nseasons`	The number of seasons to be modeled.
`season.duration`	The number of time periods in each season.
`sigma.prior`	An object created by `SdPrior` describing the prior distribution for the standard deviation of the random walk increments.
`initial.state.prior`	An object created using `NormalPrior`, describing the prior distribution of the the initial state vector (at time 1).
`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.

Returns a list with the elements necessary to specify a seasonal state model.

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

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.

bsts. SdPrior NormalPrior

  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)