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I have a time series dataset with 200 data points. I have decomposed it using the function below:

dat2 = ts(dat1, frequency = 4)
decomposeDat = decompose(dat2, "multiplicative")

I get 4 components: trend, seasonal, cyclic and irregularity. But when I check if there is seasonality present in the dataset with frequency "4", Rstudio says that there is no seasonality for this frequency. The check is performed with the following code:

dat2 = ts(dat1, frequency = 4)
fit <- tbats(dat2)
seasonal <- !is.null(fit$seasonal)
seasonal

seasonal returns FALSE meaning that there is no seasonality with frequency 4.

Can someone explain, why can I decompose it into a seasonality component when no seasonality is present from the check mentioned above?

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Without seeing your data it is hard to tell whether there is seasonality or not. The decompose() function will try to find seasonality using a different approach than tbats() as discussed in this post and the user comments of this blog post by the author of tbats.

I would recommend to post your data and discuss what you are trying to achieve to get more guidance.

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From my knowledge it decomposes the time series to a seasonal component as well since you specify it, that the seasonality is 4. Moreover, you could check the seasonality with 4 using the TStools (seasplot() function), it will provide you with a p-value of how significant is that seasonality, which seems more informative than a TRUE or a FALSE.

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