We don't know. .......

But since this is /r/AskHistorians where the mods are so damned demanding(!!!), I'll elaborate.

First of all, ghost stories are practically universal and they burst on the scene with literacy at the beginning of history, so we must assume that these stories and beliefs have prehistoric roots. Reaching back to find origins of these traditions is impossible or at least next to impossible. So we must consider the factors that encourage the universality of these stories. The core factor is clearly the universality of the human experience. In particular, we must consider the dilemma represented by death: how can people and the conscious spirit that each person represents simply cease to exist? Or more often - given the narcissist that dwells more or less in each of us - how can the world exist without ME?!?!? While many are compelled to answer that question with atheism's point of view, it is unsatisfying to many (if not most) to responding that regardless of the "how" of it, the "ceasing" part of it is simple reality. To fill this void, it is understandable that we have not only beliefs in the survival of death but stories that testify to that survival.

One of the things to remember in folklore is that we do not judge the validity of stories or belief. We simply study the stories that people tell and the beliefs they reveal. Because of that, folklorists are not in a position to explain how people "invented" belief in and stories about ghosts. Perhaps ghosts exists. Perhaps they don't. It doesn't matter. What we do know is that it is nearly universal for cultures to include the possibility of survival of death and for the dead to occasionally manifest in this world.

Because these stories and beliefs are widespread in cultures, we are better to ask about the nature of stories and how they did or might have changed over time. That is safer turf upon which to stand then to consider the origin of these traditions.

One of the first things that leaps out of these traditions is the question of corporeal versus spiritual survival. Some cultures favor the idea that ghosts are walking dead and other cultures lean more heavily on a pure spiritual return when visiting the terrestrial world. Many cultures include both elements. Usually the physical walking dead is a dreadful thing, but the spiritual return can also have its horrific elements. And there are those stories that feature a spiritual return, but a physical element nevertheless remains: the vanishing hitchhiker tells of the spirit of a child who hitches a ride and is cold so the driver gives her his sweater. He takes her to an address, only to find that the girl died a long time ago, and when he returns to the car, she and his sweater is gone, but then he goes to her grave and finds his sweater: this is a mixture of a physical presence (she takes the sweater with her) and spiritual element (she vanishes from the car).

Tracking and considering this difference as well as other features of ghosts stories and beliefs is probably a more fruitful way to consider ghosts than to attempt the pursuit of how they began - something that occurred deep in the recesses of an unfathomable past.