The Anatolian hypothesis isn't 'just speculation', but from the point of view of linguists, it's certainly much less well-supported than IE origin in the steppes of the Black and Caspian Seas.

Most recently, the pushers of the Anatolian hypothesis have taken to citing some work by Quentin Atkinson and collaborators, that uses phylogenetic models to 'show' an Anatolian origin of IE. There's an exhaustive series of criticisms at the blog Geocurrents, and the bulk of the criticism is that Atkison and co., however sophisticated their model, have deeply flawed data, both geographical and linguistic, and that whatever their model might say about the origin and spread of Indo-European languages, there's not a satisfactory account of certain linguistic evidence, like the reconstructions of the word *kwekwlo 'wheel' to Proto-Indo-European (after Anatolian split). We don't see evidence of wheeled vehicles in the archaeological record until several thousand years after the Anatolian hypothesis dates PIE, yet this word for wheels has regular reflexes in plenty of IE languages (e.g. Eng. wheel, Greek kyklos, Lithuanian kaklas, Sanskrit chakra, Tocharian kokale). Are we to believe that PIE originate in Anatolia, dispersed to western Europe and the Tarim basin, and then when wheels came along they all independently created an identical word? It's not entirely inconceivable, but for the structure of the word--it's reduplicative, from the root *kwel- 'turn', and these sorts of reduplicated nouns are very uncommon in IE. It's especially bizarre that several subgroups all choose the same root for 'turn' to modify in the same way.