Question: How do I draw specific filled regions in `DateListPlot`? I trying to plot something like this: 

![enter image description here](https://i.stack.imgur.com/Dp0LF.jpg)

Thanks

Answer: 
One approach is to use Inset.

```
DateListPlot[{1, 1, 2, 3, 5, 8, 11}, {2000, 8}, Prolog -> Inset[Graphics[{GrayLevel[.6], 
  Rectangle[Scaled[{.5, .1}], Scaled[{.7, .3}]], 
  Rectangle[Scaled[{.7, .3}], Scaled[{.9, .5}]], 
  Rectangle[Scaled[{.9, .5}], Scaled[{1.1, .7}]]}]]]

```

![enter image description here](https://i.stack.imgur.com/68Eky.png)

Some experimentation may be necessary to place multiple shaded areas in their desired locations.
Using @bbgodfrey's example

```
list = {1, 1, 2, 3, 5, 8, 11};
pnts = Thread[{AbsoluteTime /@ ({2000, #} & /@ Range[8, 14])[[3 ;; 6]], list[[3 ;; 6]]}];

DynamicModule[{pts = pnts}, LocatorPane[Dynamic[pts], DateListPlot[{1, 1, 2, 3, 5, 8, 11},
 {2000, 8}, Epilog -> {Opacity[.5, Gray], Dynamic[Rectangle @@@ Partition[pts, 2, 1]]},
 Joined -> True], Appearance -> None]]

```

[![enter image description here](https://i.stack.imgur.com/Di4HL.gif)](https://i.stack.imgur.com/Di4HL.gif)