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I'm working on the task of forecasting. The data I have is seasonal. I use exponential smoothing methods, but my references (e.g. for the Holt-Winters method) are for using such methods for seasonal and trended data.

Are there exponential smoothing methods for seasonal data without trend? Any references?

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There are of course exponential smoothing models with seasonality and without trend. Gardner's "Exponential Smoothing - The state of the art part II" (2006) is a very good overview article. You may also want to look at "Exponential Smoothing - The State Space Approach" by Hyndman et al., or this free online forecasting textbook.

In R, you can use the ets() command in the forecast package and specify model="ZNZ" to suppress trend but allow ets() to fit seasonality, if it is there.

For example, here is your result if you forecast monthly airline passengers including seasonality but excluding trend:

library(forecast)
?ets
plot(forecast(ets(AirPassengers,model="ZNZ")))

airpassengers

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