Double-Seasonal Holt-Winters Forecasting
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 )
y |
Either an |
period1 |
Period of the shorter seasonal period. Only used if |
period2 |
Period of the longer seasonal period. Only used if |
h |
Number of periods for forecasting. |
alpha |
Smoothing parameter for the level. If |
beta |
Smoothing parameter for the slope. If |
gamma |
Smoothing parameter for the first seasonal period. If
|
omega |
Smoothing parameter for the second seasonal period. If
|
phi |
Autoregressive parameter. If |
lambda |
Box-Cox transformation parameter. If |
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. |
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.
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.
Rob J Hyndman
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.
## 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) ## End(Not run)
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