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.

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.

forecast class

An object of class forecast is a list usually 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.
residuals: Residuals from the fitted model. For models with additive errors, the residuals will be x minus the fitted values.
fitted: Fitted values (one-step forecasts)

The function summary can be used to obtain and print a summary of the results, while the functions plot and autoplot produce plots of the forecasts and prediction intervals. The generic accessor functions fitted.values and residuals extract various useful features from the underlying model.

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. https://robjhyndman.com/expsmooth/.

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, 0.1))
fit <- dshw(x, 20, 5)
plot(fit)
} # }