As an Egyptologist, I can only answer about Egypt. In my answer, I will focus on annalistic material issued directly as such through the Pharaohs and their circle (royal context).
Despite the fact that early detailed records do not survive, we can say that early Egyptian royal catalogues functioned, in a way, as non-detailed annalistic records. For example, in the (fragmentary) Palermo Stone (2392–2283 BC), the earliest list of Pharaohs in Egypt, significant events in the reign of each Pharaoh are included within each "entry". Another, more detailed, piece of early Royal Annals is the so-called "genut" of Mit Rahina (Memphis), dating to the reign of Amenemhat II (The Middle Kingdom, 12th Dynasty, c. 1929–1895 BC). During the New Kingdom, the Pharaohs and their circle produce more detailed records on their deeds, destined to be placed upon visible spaces if temples and other monumental constructions, as Egypt becomes more outgoing with regards to warlike activities as well as diplomacy. Thutmose III's annals, describing his wars in Palestine, Ramesses II's Kadesh and other war-related inscriptions on various monuments and Ramesses III's Sea Peoples related texts in his funerary temple at Medinet Habu are the more prominent examples of such records, although there are much more.
With regard to Harkhuf and other autobiographical material, as well as material from Amarna, we can say that although it can function as a group of historical sources, it is not annalistic per se, as it had not been composed as such. As for Sinuhe, it may contain historical info but it is pure literature. Still, it is worth mentioning those as, in a way, they reflect a tendency of the Egyptians to move from less to more detailed sets of records adopting narrative to record historical events.
For more see
Wilkinson, Toby A. H. (2000) Royal Annals of Ancient Egypt p.23ff. New York: Columbia University Press.
The Date of the War Scenes at Karnak and the History of the Late Nineteenth Dynasty, http://eemaa.org.gr/bibliography/1072