I have a chicken-egg problem in time series:
How do we remove the deterministic trend in time series when you have a guess that the noise is non-normal? How do we check if the noise is non-normal without removing the deterministic trend?
For my time-series, when I plot the histogram of the raw values and fit a density a log-normal seems to fit very well. However, this is raw data, and it has a trend, and potential seasonality. If I remove the trend and seasonality, would the resulting density still remain a log-normal? How would I remove the trend and seasonality if I don't know the noise distribution? If my noise is indeed log-normal, then I don't think I can use an OLS regression, and have to use a GLM (which seems not to handle log-normal, somehow, but that's a separate question). Any thoughts on this, please?
I hope I have made my question clear, but please comment if you need more information.