forecast (version 8.21.1)

tbats: 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.


  y, = 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,


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.



The time series to be forecast. Can be numeric, msts or ts. Only univariate time series are supported.

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.


TRUE/FALSE indicates whether to include a trend or not. If NULL then both are tried and the best fit is selected by AIC.


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.


If y is numeric then seasonal periods can be specified with this parameter.


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.


TRUE/FALSE indicates whether or not to use parallel processing.


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.


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


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


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.


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.)


Slava Razbash and Rob J Hyndman


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



Run this code

if (FALSE) {
fit <- tbats(USAccDeaths)
plot(forecast(fit)) <- tbats(taylor)

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