Differencing and trend in time series forecasting I understand that a time series is differenced to remove trend. But if trend can be modeled for forecasting purposes then why difference a time series at all?
 A: If trend can be modeled, why difference a time series at all? That is a good question! The answer is, you do not difference the series in such instances. 
You only difference series that contain stochastic time trends, i.e. series that are cumulative sums of stationary processes (I we restrict ourselves to processes with a single unit root). You do not difference a time series that does not have a unit root, e.g. a time series with a deterministic time trend. Such series are called trend stationary. Differencing such a series creates a unit-root MA(1) component which, if neglected, messes up estimates of the other parameters in the model. This problem is called over-differencing.
A: You difference the trend in pure time series models such as ARIMA. However, there are many approaches which take care of the non-constant trend without necessarily differencing. For instance, consider ARIMAX model:
$$y_t=c+\beta t^2+\phi_1 y_{t-1}+\varepsilon_t$$
Here, you have the nonlinear trend $t^2$ and as typical autoregressive term $y_{t-1}$. This is just one approach of many possible
A: It depends on what method you use if you difference. To cite an obvious example some methods such as exponential smoothing do not require (or use) this. It is an assumption (a requirement) of ARIMA that you difference non-stationarity, but not all time series methods.
