regression.holiday {bsts} | R Documentation |
Regression Based Holiday Models
Description
Add a regression-based holiday model to the state specification.
Usage
AddRegressionHoliday(
state.specification = NULL,
y,
holiday.list,
time0 = NULL,
prior = NULL,
sdy = sd(as.numeric(y), na.rm = TRUE))
AddHierarchicalRegressionHoliday(
state.specification = NULL,
y,
holiday.list,
coefficient.mean.prior = NULL,
coefficient.variance.prior = NULL,
time0 = NULL,
sdy = sd(as.numeric(y), na.rm = TRUE))
Arguments
state.specification |
A list of state components that you wish to add to. If omitted, an empty list will be assumed. |
holiday.list |
A list of objects of type |
y |
The time series to be modeled, as a numeric vector
convertible to |
prior |
An object of class |
coefficient.mean.prior |
An object of type
|
coefficient.variance.prior |
An object of type
|
time0 |
An object convertible to |
sdy |
The standard deviation of the series to be modeled. This
will be ignored if |
Details
The model assumes that
The regression state model assumes vector of regression coefficients
contains elements
.
The HierarchicalRegressionHolidayModel assumes is
composed of holiday-specific sub-vectors
, where each
contains coefficients describing the days in
the influence window of holiday h. The hierarchical version of the
model treats
and
as parameters to be learned,
with prior distributions
and
where represents the inverse Wishart distribution.
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
.
RandomWalkHolidayStateModel
.
SdPrior
NormalPrior
Examples
trend <- cumsum(rnorm(730, 0, .1))
dates <- seq.Date(from = as.Date("2014-01-01"), length = length(trend), by = "day")
y <- zoo(trend + rnorm(length(trend), 0, .2), dates)
AddHolidayEffect <- function(y, dates, effect) {
## Adds a holiday effect to simulated data.
## Args:
## y: A zoo time series, with Dates for indices.
## dates: The dates of the holidays.
## effect: A vector of holiday effects of odd length. The central effect is
## the main holiday, with a symmetric influence window on either side.
## Returns:
## y, with the holiday effects added.
time <- dates - (length(effect) - 1) / 2
for (i in 1:length(effect)) {
y[time] <- y[time] + effect[i]
time <- time + 1
}
return(y)
}
## Define some holidays.
memorial.day <- NamedHoliday("MemorialDay")
memorial.day.effect <- c(.3, 3, .5)
memorial.day.dates <- as.Date(c("2014-05-26", "2015-05-25"))
y <- AddHolidayEffect(y, memorial.day.dates, memorial.day.effect)
presidents.day <- NamedHoliday("PresidentsDay")
presidents.day.effect <- c(.5, 2, .25)
presidents.day.dates <- as.Date(c("2014-02-17", "2015-02-16"))
y <- AddHolidayEffect(y, presidents.day.dates, presidents.day.effect)
labor.day <- NamedHoliday("LaborDay")
labor.day.effect <- c(1, 2, 1)
labor.day.dates <- as.Date(c("2014-09-01", "2015-09-07"))
y <- AddHolidayEffect(y, labor.day.dates, labor.day.effect)
## The holidays can be in any order.
holiday.list <- list(memorial.day, labor.day, presidents.day)
## In a real example you'd want more than 100 MCMC iterations.
niter <- 100
## Fit the model
ss <- AddLocalLevel(list(), y)
ss <- AddRegressionHoliday(ss, y, holiday.list = holiday.list)
model <- bsts(y, state.specification = ss, niter = niter)
## Plot all model state components.
plot(model, "comp")
## Plot the specific holiday state component.
plot(ss[[2]], model)
## Try again with some shrinkage. With only 3 holidays there won't be much
## shrinkage.
ss2 <- AddLocalLevel(list(), y)
## Plot the specific holiday state component.
ss2 <- AddHierarchicalRegressionHoliday(ss2, y, holiday.list = holiday.list)
model2 <- bsts(y, state.specification = ss2, niter = niter)
plot(model2, "comp")
plot(ss2[[2]], model2)