# Solved – Decomposing a multi seasonal time series using tbats in R

Can I decompose a time series with multiple seasonalities (an `msts` object) using `tbats` (in the `forecast` package for R) and get the random component of it? Just as getting the random component using the `decompose` function for `ts` objects?

Contents

You can use the function `tbats.components` on a `tbats` model fit. It will yield a matrix of time series containing the level, the slope and the season of the fitted model, as well as the actual observations. You can then simply subtract the components from the observations to obtain the residuals:
``> library(forecast) > fit <- tbats(USAccDeaths)  > foo <- tbats.components(fit)  > head(foo)      observed    level     slope     season [1,]     9007 9538.066 -43.81329  -823.6141 [2,]     8106 9590.489 -47.90006 -1548.1921 [3,]     8928 9642.926 -52.03042  -781.2602 [4,]     9137 9636.436 -52.12401  -528.4124 [5,]    10017 9661.657 -54.41414   304.7762 [6,]    10826 9848.610 -67.92587   815.5472  > foo[,"observed"]-foo[,"level"]-foo[,"slope"]-foo[,"season"]               Jan          Feb          Mar          Apr          May 1973  336.3616979  111.6033706  118.3650491   81.1007939  104.9810786 1974 -222.9725629 -120.0746460   65.3314214   84.8823480 -199.9296274 1975   88.0935771  -12.2533927   20.1954758 -210.2334112  194.5652535 1976   91.6890807  225.6898321 -108.3721742 -104.6956780 -128.2708712 1977   18.9462879  -59.0440990  -48.6638245    9.8410292  -38.2662635 1978  -43.2497726 -132.1089133  -25.8376148   29.8293887   34.8255629               Jun          Jul          Aug          Sep          Oct 1973  229.7689357    9.7833829   97.6213834  114.7690243   61.5528845 1974   23.6012054 -100.8973484   99.0247537   33.6304182   37.2522537 1975  -59.5136479 -162.8834589   -5.6052057 -131.8664155 -149.6577923 1976 -168.0888948   16.7956107 -130.6105420 -127.4818202  -48.5429559 1977  -81.8158991  155.2481713 -232.3853212  -95.3328947   18.0666666 1978  -82.3539729   38.3254629    8.2383295  149.0925592  -93.5561732               Nov          Dec 1973  -24.4337637 -201.9057433 1974   70.8572386 -105.5657300 1975    5.6164054 -211.3018369 1976  -94.9396877  127.1735861 1977  -34.9677557   65.1114921 1978    0.1845764  136.0468109 ``