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

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. Ignored if NULL. Otherwise, data transformed before model is estimated.

biasadj

Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities. By default, the value is taken from what was used when fitting the model.

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.

See also

HoltWinters, ets.

Examples

# NOT RUN { 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) # }