R: Double-Seasonal Holt-Winters Forecasting

dshw {forecast} | R Documentation

## Double-Seasonal Holt-Winters Forecasting

### Description

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. 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.

### 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.

### 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`.

### Author(s)

Rob J Hyndman

### 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)

    ## End(Not run)

[Package forecast version 8.2 Index]