# TBATS model (Exponential smoothing state space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components)

Source:`R/tbats.R`

`tbats.Rd`

Fits a TBATS model applied to `y`

, as described in De Livera, Hyndman &
Snyder (2011). Parallel processing is used by default to speed up the
computations.

## Usage

```
tbats(
y,
use.box.cox = NULL,
use.trend = NULL,
use.damped.trend = NULL,
seasonal.periods = NULL,
use.arma.errors = TRUE,
use.parallel = length(y) > 1000,
num.cores = 2,
bc.lower = 0,
bc.upper = 1,
biasadj = FALSE,
model = NULL,
...
)
```

## Arguments

- y
The time series to be forecast. Can be

`numeric`

,`msts`

or`ts`

. Only univariate time series are supported.- use.box.cox
`TRUE/FALSE`

indicates whether to use the Box-Cox transformation or not. If`NULL`

then both are tried and the best fit is selected by AIC.- use.trend
`TRUE/FALSE`

indicates whether to include a trend or not. If`NULL`

then both are tried and the best fit is selected by AIC.- use.damped.trend
`TRUE/FALSE`

indicates whether to include a damping parameter in the trend or not. If`NULL`

then both are tried and the best fit is selected by AIC.- seasonal.periods
If

`y`

is`numeric`

then seasonal periods can be specified with this parameter.- use.arma.errors
`TRUE/FALSE`

indicates whether to include ARMA errors or not. If`TRUE`

the best fit is selected by AIC. If`FALSE`

then the selection algorithm does not consider ARMA errors.- use.parallel
`TRUE/FALSE`

indicates whether or not to use parallel processing.- num.cores
The number of parallel processes to be used if using parallel processing. If

`NULL`

then the number of logical cores is detected and all available cores are used.- bc.lower
The lower limit (inclusive) for the Box-Cox transformation.

- bc.upper
The upper limit (inclusive) for the Box-Cox transformation.

- biasadj
Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities.

- model
Output from a previous call to

`tbats`

. If model is passed, this same model is fitted to`y`

without re-estimating any parameters.- ...
Additional arguments to be passed to

`auto.arima`

when choose an ARMA(p, q) model for the errors. (Note that xreg will be ignored, as will any arguments concerning seasonality and differencing, but arguments controlling the values of p and q will be used.)

## Value

An object with class `c("tbats", "bats")`

. The generic accessor
functions `fitted.values`

and `residuals`

extract useful features
of the value returned by `bats`

and associated functions. The fitted
model is designated TBATS(omega, p,q, phi, <m1,k1>,...,<mJ,kJ>) where omega
is the Box-Cox parameter and phi is the damping parameter; the error is
modelled as an ARMA(p,q) process and m1,...,mJ list the seasonal periods
used in the model and k1,...,kJ are the corresponding number of Fourier
terms used for each seasonality.

## References

De Livera, A.M., Hyndman, R.J., & Snyder, R. D. (2011),
Forecasting time series with complex seasonal patterns using exponential
smoothing, *Journal of the American Statistical Association*,
**106**(496), 1513-1527.