Seasonal state component

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Description

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)

Usage

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

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.

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.

Value

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

Author(s)

Steven L. Scott stevescott@google.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

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  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)

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