7

It appears they are both from a Germanic root, and the original sense for the root of guest was stranger, which would fit ghost as well as guest. (Amusingly in Latin, it ended up as hostis - enemy!)

This is a simple question, one I'm not sure belongs here. Feel free to delete it if it doesn't.

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    Yes. And to host. – Drew Jun 17 '16 at 1:55
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    @sumelic you do realize proto-germanic is not a real language right? It's just what we surmise what the earliest form of germanic languages would have been like. So the fact that the two words are only one letter away from each other in proto-germanic DOES seem to suggest that there's a possible connection. – user180089 Jun 17 '16 at 4:05
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I'm not an etymology expert, but they do not seem to be connected. I haven't found any source that links the etymology of these two words. The correspondences between Germanic languages seem to be fairly clear, and allow us to reconstruct the ancestor of "ghost" in Proto-Germanic as *gaistaz or *gaistoz and the ancestor of "guest" in Proto-Germanic as *gastiz: two distinct words.

I know of no derivational process in Indo-European languages that sticks y/i in the middle of a root, so I don't see how these words could stem from a common root of the form "g-st" or something. I guess there is still the possibility that they're both derived from a root of the form "g-" (PIE *gʰ) or that they both share a suffix "-st" or "-t," but these kind of one or two-letter coincidences aren't very strong evidence for common origin.

Here is what I've found about the etymology of these words.

Ghost

According to the Online Etymology Dictionary, "ghost" comes

from Proto-Germanic *gaistaz (source also of Old Saxon gest, Old Frisian jest, Middle Dutch gheest, Dutch geest, German Geist "spirit, ghost"). This is conjectured to be from a PIE root *gheis-, used in forming words involving the notions of excitement, amazement, or fear (source also of Sanskrit hedah "wrath;" Avestan zaesha- "horrible, frightful;" Gothic usgaisjan, Old English gæstan "to frighten").

According to the Oxford English Dictionary, "ghost" is from

Germanic type *gaisto-z. Although the word is known only in the West Germanic languages (in all of which it is found with substantially identical meaning), it appears to be of pre-Germanic formation. The sense of the pre-Germanic *ghoizdo-z, if the ordinary view of its etymological relations be correct, should be ‘fury, anger’; compare Sanskrit hḗḋas neuter anger, Avestan zōižda- ugly; the root *gheis-, *ghois- appears with cognate sense in Old Norse geisa to rage, Gothic usgaisjan to terrify (see gast v.1); outside Germanic the derivatives seem to point to a primary sense ‘to wound, tear, pull to pieces’.  

The Old English form gǽst is constant in the Exeter Book, and occurs 49 times in the Hatton MS. and 3 times in the Bodl. MS. of Alfred's translation of Gregory's Pastoral Care; it is apparently not known elsewhere. The occurrence of gǽst < *gaisti- beside gást < *gaisto- is explained by Sievers ( Ags. Gram. ed. 3) as indicating that the word, though recorded only as masculine, was originally a neuter -os, -es stem: it would thus correspond formally to the Sanskrit word quoted above.

Wiktionary says Proto-Germanic *gaistaz is

From Proto-Indo-European *ǵʰeysd-, *ǵʰisd- ‎(“anger, agitation”), from Proto-Indo-European *ǵʰyis- ‎(“bewildered, frightened”), from Proto-Indo-European *ǵʰey- ‎(“to propel, move, spin”), from Proto-Indo-European *ǵʰī- ‎(“to yawn, gape”).

I have no idea if all of this is correct. Note that even if it is, each root cited as an ancestor contains i or y.

Guest

According to the Online Etymology Dictionary, "guest" comes

from Proto-Germanic *gastiz (source also of Old Frisian jest, Dutch gast, German Gast, Gothic gasts "guest," originally "stranger"), from PIE root *ghos-ti- "stranger, guest; host" (source also of Latin hostis, in earlier use "a stranger," in classical use "an enemy," hospes "host," from *hosti-potis "host, guest," originally "lord of strangers;" Greek xenos "guest, host, stranger;" Old Church Slavonic gosti "guest, friend," gospodi "lord, master")

Wiktionary agrees that Proto-Germanic *gastiz is from Proto-Indo-European *gʰóstis, which is says is

possibly from *gʰes- ‎(“to eat”) (Sanskrit घसति ‎(ghasati))

According to the Oxford English Dictionary, "guest" is from

Germanic *gasti-z < West Aryan *ghosti-s, represented also by Latin hostis, originally ‘stranger’, in classical use ‘enemy’ (whence the compound *hosti-pot-, contracted hospit-, hospes guest, host) and by Old Church Slavonic gostĭ guest, friend. According to Brugmann, the synonymous Greek ξ-ένος is < *gh's-, weak grade of the root *ghos- represented in the Germanic word.

According to phonetic law as at present understood, the initial consonant in the Old English word must have had a palatal pronunciation, which would normally yield Middle English ȝ, modern English y. No forms with ȝ or y are, however, known to exist; the abnormal guttural pronunciation is usually explained as due to the influence of Old Norse gest-r; but the occurrence of hybrid forms like gist, gust /ʏ/ in the S.W. dialects of the 13th cent. is hard to account for on this supposition.

My own thoughts

What follows is subjective and probably not that useful, but I'll try to summarize what I think. It seems phonologically impossible for Modern English /goʊst/ to descend from Proto-Indo-European *ghosti-s/Proto-Germanic *gastiz (the root meaning "stranger"). The sound changes do not work out, in English or in any other languages from which English might have got this word as a loan. So even if the idea of a semantic change "stranger" > "ghost" seems plausible, this does not work as an explanation of the etymology of these words.

It seems a bit more possible from a phonological perspective for "guest" to have descended from Proto-Germanic *gaistaz or *gaistoz. This is not possible following regular English sound changes from Proto-Germanic, but we already know from the initial consonant that this word did not develop totally regularly in English, and that it may have been influenced by borrowing from other Germanic languages (some of which have "e"-like vowels in the descendants of *gaistaz). But the words in other Germanic languages that are descended from *gaistaz all basically mean "ghost." Semantically, there is not a good match between the meaning of "guest" and the meanings of other words believed to be descended from *gaistaz, and there is a very good match between the meaning of "guest" and the meanings of other words that are believed to be descended from *gastiz.

It doesn't seem particularly likely to me that a root originally meaning "to wound/tear apart" or "fury" (in Proto-Indo-European), and "ghost" later on (in Proto-Germanic), would then develop the meaning of "guest." Of course, many odd semantic changes are possible, and are postulated due to other convincing evidence of an etymological relationship between words, but there isn't any convincing evidence of a connection in this case.

2

Quoting from David W. Anthony's "The Horse, The Wheel, and Language", 2007, page 303:

The Yamnaya horizon is the visible archaeological expression of a social adjustment to high mobility — the invention of the political infrastructure to manage larger herds from mobile homes based in the steppes. A linguistic echo of the same event might be preserved in the similarity between English guest and host. They are cognates, derived from one Proto-Indo-European root (*ghos-ti-). (A "ghost" in English was originally a visitor or guest.) The two social roles opposed in English guest and host were originally two reciprocal aspects of the same relationship. The late Proto-Indo-European guest-host relationship required that "hospitality" (from the same root through Latin hospes 'foreigner, guest') and "friend-ship" (*ieiwas-) should be extended by hosts to guests (both *ghos-ti-) in the knowledge that the receiver and giver of "hospitality" could later reverse roles. The social meaning of these words was then more demanding than modern customs would suggest. The guest-host relationship was bound by oaths and sacrifices so serious that Homer's warriors, Glaukos and Diomedes, stopped fighting and presented gifts to each other when they learned that their grandfathers had shared a guest-host relationship. This mutual obligation to provide "hospitality" functioned as a bridge between social units (tribes, clans) that had ordinarily restricted these obligations to their kin or co-residents (*h4erós-). Guest-host relationships would have been very useful in a mobile herding economy, as a way of separating people who were moving through your territory with your assent from those who were unwelcome, unregulated, and therefore unprotected. The guest-host institution might have been among the critical identity-defining innovations that spread with the Yamnaya horizon.

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