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I have time series with daily data. This time series have frequency 7. Before I start with modeling first I made seasonal adjusted series with STL decomposition (from forecast package). So next step should be modeling with models from forecast package like auto.arima,snaive,ets,tbats etc

So my question is does I can use BoxCox transformation during modeling or not, with this seasonally adjusted series ?

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Rather than asking how to approach this this issue in "this way" , I suggest that you follow the standard approach of model identification and model diagnostic checking culminating in a model with statistically significant parameters and an error process that can't be proven to be non-gaussian.

I suggest that you follow the tried and trusted paradigm here OR something close to it. https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf

Is there any Forecasting algorithm or way to forecast the daily data available only on working days only(i.e Mon to Fri)? will also be of some help as seasonality of "7" usually suggests data driven by "human habits" that are often suggest some deterministic structure in addition to memory.

In specific BOX-COX can be useful if the variance of the errors is correlated with the expected value. As often as not the error variance can change at particular points in time suggesting a Weighted Least Squares approach level as detailed by TSAY here http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html . For an overview of power transforms possibly suggested by the Box-Cox test look at my response here When (and why) should you take the log of a distribution (of numbers)?

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