forecast (version 5.7)

dshw: Double-Seasonal Holt-Winters Forecasting

Description

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

Usage

dshw(y, period1, period2, h=2*max(period1,period2), 
    alpha=NULL, beta=NULL, gamma=NULL, omega=NULL, phi=NULL, 
    lambda=NULL, 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. Ignored if NULL. Otherwise, data transformed before model is estimated.

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".

  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 meanf.

  An object of class "forecast" is a list containing at least 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 (either object itself or the time series used to create the model stored as object).
• residuals
  Residuals from the fitted model. That is x minus fitted values.
• fitted
  Fitted values (one-step forecasts)

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 Reseach 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.

See Also

HoltWinters, ets.

Examples

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)