We have no proof of ghosts.
It's entirely possible that we won't unless science can find a way to interact with the phenomena, repeatedly be able to direct it (if it's intelligent) and get answers that are verifiable.
What we often get is a wide variety of evidence which for the greater part includes anecdotal stories by witnesses, some video and photography as well as sound recordings and meter readings. This is evidence of something, but until every single possible explanation is disproved, it still isn't a ghost (whatever that truly is).
It's a vicious circle.
We might be tackling investigations the entirely wrong way by believing we must have evidence to parade around and fit into the "haunted" conclusion. If you believe a place is haunted, you get unusual findings in that place, you add them up as proof of haunting. The fact is, the house I grew up in had a raccoon in the attic. The house was very haunted, but the raccoon also added an element of what anyone visiting would assume was an evil spirit scratching and thumping and making a ruckus. A visitor would easily run from the place in a fright at the sound of that within the context of a known haunted building. By gathering evidence in a place reported to be haunted, bias is going to happen and deep down inside, investigators hope "this is the one" that is actually haunted - finally.
I'm also in the realm of Bigfoot research, and one thing you learn in that arena, is that a weekend guy going out poking around the woods for Bigfoot is not going to find them. But, the guy who sits in his farmhouse on the edge of the forest, is going to be plagued by them. They're used to him. They're used to his family. They know the routine. But, you send a hiker into the woods, the woods go still and cloaked. The same goes for haunted homes. They do not show themselves often for a team that rolls in to do a several-hour study.
A true haunting can only be determined by long-term observation inside of a place. One has to live it. He must immerse himself in the building and, over a period of time, determine that there is a regularity to strange phenomena that when added all together shows an active environment. We cannot go in one night to a stranger's home and determine haunting.
If we separate our desire to find "proof" and shift to finding "possibilities," we will do better in our pursuit of understanding ghostly phenomena. Unfortunately, popular TV ghost hunters set a standard of wanting video, audio and electrician's tools readings to prove a haunting. We must move from finding support of a place being haunted to simply studying its behaviors, silently stalking the phenomena to anticipate, activate, instigate, and understand.
As a psychometrist, when I teach people how to hold an object and read the past information it possesses, I tell them to not let the intellect get in the way. The intellect says, "this is a ring with a nice stone, looks antique, probably a family heirloom." No! Hold it without focusing on what it is, how it looks, what it might mean visually. Let the object tell you what it is. So it goes with ghost hunting, it is best to tackle the set of phenomena as its physical outcome without attributing it to traditional views of ghosts and souls of the dead. Say, "I have no idea where this came from, but what are the possibilities?" By staying only on the traditionalist view of ghosts and the old wive's tales about them, we miss a huge area of research.
The reason we are at a bottleneck in understanding the ghost realm is because people have ended up in this cul-de-sac of the mind about what ghosts are, how they work, and why they are here.
We must maintain our minds on a throughway that allows for all possibilities to go back and forth. Don't look to books and others to tell us what the phenomena is. Let the phenomena tell us.
We do not have proof of ghosts. And, ironically, we may never know what ghosts are so long as we continue to think we know what they are and attack them from that belief system.