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.

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 transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.

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.

See also

tbats.components().

Author

Slava Razbash and Rob J Hyndman

Examples

if (FALSE) { # \dontrun{
fit <- tbats(USAccDeaths)
plot(forecast(fit))

taylor.fit <- tbats(taylor)
plot(forecast(taylor.fit))
} # }