Does there exist model (ideally implemented in R) which take into account multiseasonality for multivariate time series as BATS does in the univariate case?
Found a possible answer for you at this link, which could provide you with more information on the specific package you are looking for. According to the author, you may want to look into
msts as a package for handling your type of data:
An alternative is to use a
mstsobject (defined in the
forecastpackage) which handles multiple seasonality time series. Then you can specify all the frequencies that might be relevant. It is also flexible enough to handle non-integer frequencies.
As an example, below is an example on how to handle multiseasonality, using
taylor electricity dataset (from
forcast package) with daily ($24 \times 2$) and weekly ($24 \times 2 \times 7$) cycles:
x <- msts(taylor, seasonal.periods=c(24*2,24*2*7)) fit <- tbats(x[1:1000]) plot(forecast(fit))
Additionally, in case you may want to use dummy variables as @TomWitten suggests, you can view the information on this page, which deals with forecasting double (or multiple) seasonal multivariate time series, with specific examples.
if you know the seasonality could you not just create a series of dummy variables to capture the effects? In my time series data i had 12 monthly dummies for example