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In De Liv­era, Hyndman & Snyder (2011), a TBATS model (exponential smoothing state space model with Box-Cox transformation, ARMA errors, trend and seasonal components) for additive seasonality has been discussed. Can TBATS be used with multiplicative seasonality? Are there any restraints or numerical difficulties in TBATS or BATS with multiplicative seasonality?

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    $\begingroup$ Please, could you provide a link for Hyndman (2011)'s research, or at least provide its full reference. What is a tbats model? Thank's $\endgroup$ – Andre Silva Jun 15 '13 at 12:40
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    $\begingroup$ Since @RobHyndman published 11 papers in 2011, "Hyndman (2011)" doesn't really pin it down. However, tbats is a function in the forecast package in R and it refers to this paper. I will edit the question to include a link. $\endgroup$ – Glen_b Jun 15 '13 at 23:32
  • $\begingroup$ BATS and TBATS extend ETS models. This answer suggests looking at Hyndman et al (2008) for those (again, just giving a year for Rob doesn't really narrow it down), which I presume was intended to mean this book. $\endgroup$ – Glen_b Jun 15 '13 at 23:44
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The Box-Cox transformation includes logarithms, and logarithms with additive components is equivalent to multiplicative components on the original scale. There would be no point mixing Box-Cox transformations and multiplicative components.

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