I have the following time series data observed daily:
series <- c(10, 25, 8, 27, 18, 21, 12, 9, 31, 18, 8, 30, 14, 13, 10, 14,
14, 14, 6, 9, 22, 21, 22, 8, 7, 6, 22, 21, 36, 16, 2, 13, 23,
40, 12, 27, 18, 10, 11, 37, 44, 30, 40, 25, 13, 11, 58, 56, 46,
39, 28, 27, 19, 20, 97, 90, 70, 73, 30, 22, 97, 34)
and want to fit it using tbats from the R forecasts package. I also want to model it with weekly correlation:
library(forecast)
x.msts = msts(series,seasonal.periods = 7)
model <- tbats(x.msts)
# shows "--- loading profile ---"
Examing/plotting the model with str reveals a huge fitted variance of 4.9e+17.
And, plotting the forecast going forward, we observe massive swings:
> forecast(model)$mean
Multi-Seasonal Time Series:
Start: 9 7
Seasonal Periods: 7
Data:
[1] 1.483789e+44 -1.399297e+42 -2.566455e+44 -1.374316e+43 -1.527758e+38
[6] 2.036194e+42 5.639596e+42 8.231600e+40 -2.578859e+41 -1.355840e+43
Are these estimates the "correct" solution to the TBATS model fitting procedure, or is there a bug in the forecast package? If not a bug, can someone help me understanding mathematically why this normal-looking time series produces these estimates?
This is my first post on CV so apologies if this should be on SO!
I have filed a bug report on github
Also some people have noticed that I'm not using multiple seasonality factors, so I want to show here that the bug is still an issue:
x2.msts <- msts(series,seasonal.periods = c(7,30))
model_x2_1 <- tbats(x2.msts) # high variance
model_x2_2 <- tbats( series, seasonal.periods = c(7,30) ) # also high variance
This is perhaps the same problem as described here, so the reason is presumably a bug in the forecast package. I'm not sure if the following alternative will give you the desired result, but you can leave series as is and put seasonal.periods=7 in the call of tbats:
library(forecast)
series <- c(10, 25, 8, 27, 18, 21, 12, 9, 31, 18, 8, 30, 14, 13, 10, 14,
14, 14, 6, 9, 22, 21, 22, 8, 7, 6, 22, 21, 36, 16, 2, 13, 23,
40, 12, 27, 18, 10, 11, 37, 44, 30, 40, 25, 13, 11, 58, 56, 46,
39, 28, 27, 19, 20, 97, 90, 70, 73, 30, 22, 97, 34)
x.msts <- msts(series,seasonal.periods = 7)
model_1 <- tbats(x.msts)
model_2 <- tbats( series, seasonal.periods = 7 )
The variance of model_2 is much better than that of model_1:
> str(model_1)
List of 19
$ lambda : num 0.21
$ alpha : num 0.374
$ beta : NULL
$ damping.parameter: NULL
$ gamma.values : NULL
$ ar.coefficients : num [1:2] 1.296 -0.911
$ ma.coefficients : num [1:2] -1.62 0.98
$ likelihood : num 549
$ optim.return.code: int 0
$ variance : num 4.9e+17
$ AIC : num 571
$ parameters :List of 2
..$ vect : num [1:6] 0.21 0.374 1.296 -0.911 -1.615 ...
..$ control:List of 6
.. ..$ use.beta : logi FALSE
.. ..$ use.box.cox : logi TRUE
.. ..$ use.damping : logi FALSE
.. ..$ length.gamma: num 0
.. ..$ p : int 2
.. ..$ q : int 2
$ seed.states : num [1:5, 1] 4.16 0 0 0 0
$ fitted.values : Time-Series [1:62] from 1 to 9.71: 19.97 19.28 4.53 21.83 56.15 ...
..- attr(*, "msts")= num 7
$ errors : Time-Series [1:62] from 1 to 9.71: -1.206 0.496 0.828 0.415 -2.354 ...
..- attr(*, "msts")= num 7
$ x : num [1:5, 1:62] 3.71 -1.21 0 -1.21 0 ...
$ seasonal.periods : NULL
$ y : Time-Series [1:62] from 1 to 9.71: 10 25 8 27 18 21 12 9 31 18 ...
..- attr(*, "msts")= num 7
$ call : language tbats(y = x.msts)
- attr(*, "class")= chr "bats"
>
.
> str(model_2)
List of 23
$ lambda : num 0.198
$ alpha : num 0.198
$ beta : NULL
$ damping.parameter: NULL
$ gamma.one.values : num -0.0157
$ gamma.two.values : num 0.00991
$ ar.coefficients : NULL
$ ma.coefficients : NULL
$ likelihood : num 553
$ optim.return.code: int 0
$ variance : num 0.969
$ AIC : num 571
$ parameters :List of 2
..$ vect : num [1:4] 0.19842 0.19782 -0.0157 0.00991
..$ control:List of 6
.. ..$ use.beta : logi FALSE
.. ..$ use.box.cox : logi TRUE
.. ..$ use.damping : logi FALSE
.. ..$ length.gamma: int 2
.. ..$ p : num 0
.. ..$ q : num 0
$ seed.states : num [1:5, 1] 4.1851 0.3176 0.0103 -0.5806 0.4447
$ fitted.values : Time-Series [1:62] from 1 to 62: 25.1 20 11.1 10.2 24.3 ...
$ errors : Time-Series [1:62] from 1 to 62: -1.594 0.41 -0.507 1.697 -0.552 ...
$ x : num [1:5, 1:62] 3.87 -0.231 0.456 -0.626 -0.125 ...
$ seasonal.periods : num 7
$ k.vector : int 2
$ y : Time-Series [1:62] from 1 to 62: 10 25 8 27 18 21 12 9 31 18 ...
$ p : num 0
$ q : num 0
$ call : language tbats(y = series, seasonal.periods = 7)
- attr(*, "class")= chr [1:2] "tbats" "bats"
>