Add discussion about needing future values

notebooks/seasonality,_holiday_effects,_and_regressors.ipynb

@@ -1195,9 +1195,9 @@
     "\n",
     "[This notebook](https://nbviewer.jupyter.org/github/nicolasfauchereau/Auckland_Cycling/blob/master/notebooks/Auckland_cycling_and_weather.ipynb) shows an example of using weather factors as extra regressors in a forecast of bicycle usage, and provides an excellent illustration of how other time series can be included as extra regressors.\n",
     "\n",
-    "The `add_regressor` function has optional arguments for specifying the prior scale (holiday prior scale is used by default) and whether or not the regressor is standardized - see the docstring with `help(Prophet.add_regressor)` in Python and `?add_regressor` in R. Note that regressors must be added prior to model fitting.\n",
+    "The `add_regressor` function has optional arguments for specifying the prior scale (holiday prior scale is used by default) and whether or not the regressor is standardized - see the docstring with `help(Prophet.add_regressor)` in Python and `?add_regressor` in R. Note that regressors must be added prior to model fitting. Prophet will also raise an error if the regressor is constant throughout the history, since there is nothing to fit from it.\n",
     "\n",
-    "The extra regressor must be known for both the history and for future dates. It thus must either be something that has known future values (such as `nfl_sunday`), or something that has separately been forecasted elsewhere. Prophet will also raise an error if the regressor is constant throughout the history, since there is nothing to fit from it.\n",
+    "The extra regressor must be known for both the history and for future dates. It thus must either be something that has known future values (such as `nfl_sunday`), or something that has separately been forecasted elsewhere. The weather regressors used in the notebook linked above is a good example of an extra regressor that has forecasts that can be used for future values. One can also use as a regressor another time series that has been forecasted with a time series model, such as Prophet. For instance, if `r(t)` is included as a regressor for `y(t)`, Prophet can be used to forecast `r(t)` and then that forecast can be plugged in as the future values when forecasting `y(t)`. A note of caution around this approach: This will probably not be useful unless `r(t)` is somehow easier to forecast then `y(t)`. This is because error in the forecast of `r(t)` will produce error in the forecast of `y(t)`. One setting where this can be useful is in hierarchical time series, where there is top-level forecast that has higher signal-to-noise and is thus easier to forecast. Its forecast can be included in the forecast for each lower-level series.\n",
     "\n",
     "Extra regressors are put in the linear component of the model, so the underlying model is that the time series depends on the extra regressor as either an additive or multiplicative factor (see the next section for multiplicativity)."
    ]