I made a time series decomposition with tbats. There is weekly and yearly seasonality in the data (and maybe also monthly – not really important for the question)
x <- msts(data, start=c(2005,1,1), seasonal.period=c(7,30.4,365.25)) fit <- tbats(x, use.box.cox=FALSE) plot(fit) 
As far as i understand the tbats result is an "additive decomposition", right?
I can now access the different parts of the tbats decomposition:
level <- as.numeric(tbats.components(fit)[,'level']) season1 <- as.numeric(tbats.components(fit)[,'season1']) season2 <- as.numeric(tbats.components(fit)[,'season2']) season3 <- as.numeric(tbats.components(fit)[,'season3']) Since i suppressed 'Box-Cox transformation' earlier, level is roughly the same then trend according to a post from Rob J Hyndman in the comments section here: here
In order to get the remainder part of the decomposition is it a legit way to just subtract all the parts from the original data?
remainder <- data - level - season1 - season2 - season3 What do i get when i use this:
y <- resid(fit) I am a bit confused right now about the right way to do it… Many thanks for all your input!
Update:
resid(fit) fit$errors Those two are both the same. I guess these values are related to the tbats method. I am doubting that i can take them as the "remainder" of the decomposition? Is there a way to extract the remainder out of the tbats method? In his paper 'Forecasting time series with complex seasonal patterns using exponential smoothing' Rob J Hyndman shows remainder graphs for the tbats method so that's why i think it is possible to get in R as well.
Anyone any thoughts about that?
Best Answer
A TBATS model has an ARMA error structure. You are ignoring that when you simply subtract the level and seasonal terms. The residuals() function will extract the residuals properly, taking account of the ARMA error structure.