Where were Malays originated?

Malays (Malay: Melayu) are an ethnic group of Austronesian peoples predominantly inhabiting the Malay Peninsula and parts of Sumatra and Borneo. The Malay ethnic group is distinct from the concept of a Malay race, which encompasses a wider group of people, including most of Indonesia and the Philippines. The Malay language is a member of the Austronesian family of languages.

History
The Malay people are believed to have originated in Borneo and then expanded outwards into Sumatra and later into the Malay Peninsula. These people were descendants of Austronesian-speakers who migrated from the Philippines and originally from Taiwan. The main foundation of this school of thought lies in the fact that the oldest Malay settlements have been discovered in Sumatra and not in the Malay Peninsula. This suggests an upward - south to north - migratory route. Malay culture reached its golden age during Srivijayan times. Malays practiced Buddhism, Hinduism, and their native Animism before converting to Islam in the 15th century.

Etymology
According to the History of Jambi, the word Melayu originated from a river with name Melayu River near to Batang Hari River of today's Muara Jambi, Jambi province of Sumatra, Indonesia. The founder of Malacca, Parameswara was a prince of Palembang which was once owned by a nation called "Malayu" back in the seventh century. Yi Jing (635-713) clearly recorded in his journal book a nation of name 'Ma-La-Yu' existed. According to archaeological research of Jambi, large numbers of ancient artifacts and ancient architectures of Melayu have been found with photo evidence.

The word "Malay" was adopted into English via the Dutch word "Malayo", itself from Portuguese "Malaio", which originates from the Malay word "Melayu". According to one popular theory, the word Melayu means "migrating" or "fleeing", which might refer to the high mobility of these people across the region.

Another theory holds that the name refers to the Tamil word Malai Yur which means "Land of Mountains" (malai means mountain and yur means land), a reference to the hilly nature of the Malay Archipelago.

Source: Wikipedia