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How can I specify a trend (term) in my time series data? does it have a logical procedure or is it totally base on visual interpretation of historical plot?

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If you have a time series with enough observations on a long time interval, so that in case of seasons in your data, many seasons will be included then you can perform a dickey-fuller test which checks for non-stationary of your data. This is a common way to check if there is a trend in your data.

What is often done in order to determine the trend 'coefficient' is then to compute a moving average (choose a good rolling window yourself) and on this moving average you can then fit a linear regression (in case of linearity of your trend).

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