# tbats

From forecast v6.0
by Rob Hyndman

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

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.

- Keywords
- ts

##### Usage

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

##### 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.
- ...
- 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 wi

##### 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, {,..., }) 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.

##### See Also

##### Examples

```
fit <- tbats(USAccDeaths, use.parallel=FALSE)
plot(forecast(fit))
taylor.fit <- tbats(taylor)
plot(forecast(taylor.fit))
```

*Documentation reproduced from package forecast, version 6.0, License: GPL (>= 2)*

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