A person born in December 1984 would be 33 going on 34 years old in 2018, would have had one Saturn return, and be coming to the end of his third Jupiter-cycle.
The method used in western Tropical Astrology to narrow down your birth time is called “Chart Rectification.” This consists of looking at major events in a persons lifetime, and then comparing them with transits made by (e.g.) Saturn and / or Jupiter to that person’s natal chart.
If a major event corresponds to a planet transitting a -known- feature of the Natal chart, we may ignore that event for the purpose of Chart Rectification.
If however a major event does not correspond to such a feature, that is evidence that one has discovered a previously unknownfeature of the Natal chart – such as the exact position of the Ascendant or Mid-Heaven. We can verify this to see whether the position of the Ascendant would fit in with the known-facts (given the data supplied in the original question, the Ascendant can be narrowed down to a range of 22º 30′ – the maximum amount by which it would change position in ninety minutes).
For example: if one experienced a major life-affecting illness, AND that particular time did not correspond with Saturn transitting anywhere or anything else in your chart, that might show that Saturn was transitting your Ascendant at that time. Alternatively, if you experienced major good fortune in your public life, and Jupiter was not transitting anywhere or anything else in your chart, that might show that Jupiter was in fact transitting your Mid-Heaven.
By thus working out the precise moment of your Ascendant and / or Mid Heaven, it is then possible to work out your exact time of birth by back-calculation.
See also:
Sol Ascendans - The Website of Alex Sumner 