Roger Beck, The Religion of the Mithras Cult in the Roman Empire: Mysteries of the Unconquered Sun, Oxford University Press, 2006, makes the following interesting remark on p.209-10:
… the nominal solstice on 25 December, becomes the Sun’s birthday, the ‘Natalis Invicti’, as the Calendar of Filocalus famously notes—to which phrase in Greek (heliou genethlion) the less well-known Calendar of Antiochus appends ‘light increases’ (auxei phos). According to Macrobius (Sat. 1.18.10), not only was the Sun’s birthday celebrated at the winter solstice but he was also displayed as a baby on that day:
These diverences in age [in the representations of various gods] relate to the Sun, who is made to appear very small (parvulus) at the winter solstice. In this form the Egyptians bring him forth from the shrine on the set date to appear like a tiny infant (veluti parvus et infans) on the shortest day of the year.
16. Calendar of Filocalus, Salzman 1990: 149–53; Calendar of Antiochus, Boll 1910: 16, 40–4.
Boll, F. 1910. Griechische Kalender: 1. Das Kalendarium des Antiochos, Sitzungsberichte der Heidelberger Akademie der Wissenschaften, philos.-hist. Klasse, Jahrgang 1910, 16. Abhandlung (Heidelberg).
The “Calendar of Filocalus” is our familiar Chronography of 354, part 6, which I placed online long ago here. As we all know, for 25 Dec. it has “Natalis Invicti” against the day. But the Calendar of Antiochus is not known to me. I wonder if it is online? Beck also tells us that this is Antiochus of Athens, an astrologer, whose works must exist — Beck references them as CCAG 4, etc, which turns out to be Catalogus Codicum Astrologorum Graecorum. The CCAG turns out to be an old work, and some of it is online at Archive.org.
The only real reference to the calendar that I could find online was in D.M.Murdock (Acharya S), Christ in Egypt: The Horus-Jesus connection, p.89, online in preview here (and I know we all wince at the standards of this source, but this new book is much better referenced). This tells me that the calendar was published indeed by Boll in 1910; that it records the solstice on 22nd December, and dates to ca. 200 AD.