Double-Seasonal Holt-Winters Forecasting
Returns forecasts and prediction intervals using Taylor's (2003) Double-Seasonal Holt-Winters method.
dshw(y, period1, period2, h=2*max(period1,period2), alpha=NULL, beta=NULL, gamma=NULL, omega=NULL, phi=NULL, lambda=NULL, armethod=TRUE)
- a numeric vector or time series
- Period of the shorter seasonal period.
- Period of the longer seasonal period.
- Number of periods for forecasting
- Smoothing parameter for the level.
- Smoothing parameter for the slope.
- Smoothing parameter for the first seasonal period.
- Smoothing parameter for the second seasonal period.
- Autoregressive parameter.
- Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated.
- If TRUE, the forecasts are adjusted using an AR(1) model for the errors.
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
- An object of class "
summaryis used to obtain and print a summary of the results, while the function
plotproduces a plot of the forecasts and prediction intervals.
The generic accessor functions
residualsextract useful features of the value returned by
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 lower Lower limits for prediction intervals upper Upper limits for prediction intervals level The confidence values associated with the prediction intervals x The original time series (either
objectitself or the time series used to create the model stored as
residuals Residuals from the fitted model. That is x minus fitted values. fitted Fitted values (one-step forecasts)
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,
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)