Double-Seasonal Holt-Winters Forecasting

Returns forecasts using Taylor's (2003) Double-Seasonal Holt-Winters method.

Usage

dshw(
  y,
  period1 = NULL,
  period2 = NULL,
  h = 2 * max(period1, period2),
  alpha = NULL,
  beta = NULL,
  gamma = NULL,
  omega = NULL,
  phi = NULL,
  lambda = NULL,
  biasadj = FALSE,
  armethod = TRUE,
  model = NULL
)

Arguments

y: Either an msts object with two seasonal periods or a numeric vector.
period1: Period of the shorter seasonal period. Only used if y is not an msts object.
period2: Period of the longer seasonal period. Only used if y is not an msts object.
h: Number of periods for forecasting.
alpha: Smoothing parameter for the level. If NULL, the parameter is estimated using least squares.
beta: Smoothing parameter for the slope. If NULL, the parameter is estimated using least squares.
gamma: Smoothing parameter for the first seasonal period. If NULL, the parameter is estimated using least squares.
omega: Smoothing parameter for the second seasonal period. If NULL, the parameter is estimated using least squares.
phi: Autoregressive parameter. If NULL, the parameter is estimated using least squares.
lambda: Box-Cox transformation parameter. If lambda="auto", then a transformation is automatically selected using BoxCox.lambda. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.
biasadj: Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.
armethod: If TRUE, the forecasts are adjusted using an AR(1) model for the errors.
model: If it's specified, an existing model is applied to a new data set.

Value

An object of class "forecast" which is a list that includes the following elements:

model: A list containing information about the fitted model
method: The name of the forecasting method as a character string
mean: Point forecasts as a time series
x: The original time series.
residuals: Residuals from the fitted model. That is x minus fitted values.
fitted: Fitted values (one-step forecasts)

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by dshw.

Details

Taylor's (2003) double-seasonal Holt-Winters method uses additive trend and multiplicative seasonality, where there are two seasonal components which are multiplied together. For example, with a series of half-hourly data, one would set period1=48 for the daily period and period2=336 for the weekly period. The smoothing parameter notation used here is different from that in Taylor (2003); instead it matches that used in Hyndman et al (2008) and that used for the ets function.

References

Taylor, J.W. (2003) Short-term electricity demand forecasting using double seasonal exponential smoothing. Journal of the Operational Research Society, 54, 799-805.

Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer-Verlag. http://www.exponentialsmoothing.net.

Author

Rob J Hyndman

Examples


if (FALSE) { # \dontrun{
fcast <- dshw(taylor)
plot(fcast)

t <- seq(0,5,by=1/20)
x <- exp(sin(2*pi*t) + cos(2*pi*t*4) + rnorm(length(t),0,.1))
fit <- dshw(x,20,5)
plot(fit)
} # }