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. 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.

### 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 8.12 Index]