I have a dataset of daily demand over the last 2 years. The data has weekly seasons and nested daily seasons. I converted the data into a time series using ts function with frequency=365. When using HoltWinters method now, he interprets every day as an own season, resulting in non-robust outcomes. How can I tell him to only include 59 seasons (52 weekly and 7 daily seasons)?
First of all, weekly seasonality means that a pattern may repeats itself every week. Daily seasonality means that a pattern may repeat itself every day. To allow your model to contain daily seasonality you need a higher frequency time series than daily. I assume that with the '52 weekly and 7 daily seasons' you mean that you want to specify 52 seasonal factors for your annual seasonality and 7 seasonal factors (logically) for your weekly seasonality.
The frequency specifies the number of observations per cycle (season). With daily data a weekly seasonality is introduced by:
ts(x, frequency = 7)
You might want to restrict yourself to use just that. (https://robjhyndman.com/hyndsight/dailydata/)
Instead of the ts object, you can use the msts (Multi-Seasonal Time Series) object as follows to specify weekly and annual seasonality.
msts(x, seasonal.periods = c(7, 365.25))
Or omit leap day observations and just use 365. You can use bats or tbats:
y <- msts(x, seasonal.periods=c(7,365.25))
fit <- tbats(y)
fc <- forecast(fit)
plot(fc)
You should have a look at https://robjhyndman.com/hyndsight/dailydata/
Hope this helps.