ARIMA with and without Box-Cox transformation

I refer to Prof Rob Hyndman forecasting online book, and would like to ask you about the ARIMA forecasting with and without Box-Cox transformation.

What I have understood from book is that, Box-Cox transformation give positive forecast interval and to stabilize the variance.

When I applied in my project, my forecasting with Box-Cox transformation is abit weird compared to without transformation. May I ask why the Box-Cox transformation gave different from normal ARIMA?

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