The Oldest Traditional Buddhist Lineage?

In Hinduism the traditional master-disciple relationship in the transmission is very important, which means that a student can go and learn from a teacher [whose initiatory lineage goes back directly to Adi Shankara](https://en.wikipedia.org/wiki/Shankaracharya) for example. I would have liked to know if there was such a thing in Buddhism, and if so, what were the oldest lineages still in place? With the master-disciple initiation chain unbroken. Is there one that can be traced back to the Buddha himself? I hear a lot about the Forest Tradition, [but it only dates back to the 20th century](https://en.wikipedia.org/wiki/Thai_Forest_Tradition#Formative_period_(around_1900)) .