The region stretching from Kazakhstan through Mongolia to Manchuria is the home to some truly remarkable nations. Traditionally, people here have been highly mobile tribes of pastoral nomads. When not tending their herds, they would practice the arts of war, raiding one another. If your ancestors lived in any part of this broad region in CE 1000, their ancestors were probably spread all across it in CE 1.
At certain times, they have become united and directed their energies outward, migrating into and ruling surrounding nations, including China, Afghanistan, Northern India, Iran, Russia, the Ukraine, and even pieces of Central Europe. This has happened four times:
Ironically, if your ancestors are from Kazakhstan or Mongolia, none of this really matters, since people were generally leaving Central Asia, not flowing in. There are some exceptions, however:
Seventh Century: The beginning of the Tang dynasty was a golden age for China. At this time, Turks had settled in China and made up a large part of the Chinese army. Seeking to control them, the Chinese conquered and ruled their Central Asian homeland. A small Chinese aristocracy ruled there for over a century. If your ancestors lived here in CE 1000, their ancestors might have lived both there and in central China in 500 CE.
751: An ethnically Iranian army led by Arab officers defeated the Turks and Chinese, seizing Central Asia for the Umayyad Caliphate. From this point, an Iranian (Persian) aristocracy ruled Central Asia. If your ancestors lived here in CE 1000, their ancestors could have lived both there and in Iran, Iraq, or Arabia in 500 CE.
The thirteenth century: Genghis Khan, in person, takes over Central Asia, which becomes his first major conquest in the growing Mongol Empire. Now a Mongolian upper class rules. The Mongols were noteworthy for promoting an excellent communication system and for recruiting talented people from all over their empire for important posts. Thus, if your ancestors were in Central Asia in CE 1490, they could have been from anywhere in the Mongol empire in CE 1000.
The nineteenth century: Central Asia became part of Russia's cosmopolitan Empire. If your ancestors were in Central Asia in 1900, they could easily have had ancestors in European Russia in 1800. Family folklore should help you sort this out.