If there is no ground wire, then your DirecTV dish installer people did it wrong. There is supposed to be a ground wire that attaches to an included grounding block that's inline with the antenna cables. It's a small hunk of metal with female connectors for your antenna cables. There will be an actual thread for the ground screw right on the grounding block. The screw itself is usually painted a unique color such as dark green or dark blue. I'm not sure if the paint is just a marking or if it's anti-corrosion paint or what, but the kits always have them.

The grounding block is not necessarily right on, or next to, the antenna. It's possible that it's under your house or in your attic somewhere. You need to trace the antenna cables before assuming it's not there.

From the grounding block, the thick copper ground wire runs to any seriously-grounded point in the house. If it's convenient, you can ground it to the official ground point in your electrical service box. If not, you can find a bit of plumbing and attach a ground strap to that.

When I grounded my replacement roof antenna, I connected its ground wire to the direcTV grounding block, and grounded that block to the plumbing.

The purpose of the ground wire is to provide a path for the inevitable static electricity that builds up when the wind blows across your antenna. If you don't provide this ground path, then the static electricity will reach ground via the antenna signal cable (i.e., through your equipment).

By the way, do you have the 3-LNB antenna for the HD feed? My antenna has 3 LNBs and four outputs (and the grounding block has four wire points), so I can run two receivers (such as both an HD and an SD tivo) from the antenna without needing a separate multiplexer box.