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`

" 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`

.

## 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.

## 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.