Old Testament prophecies are sometimes 'thematic', by 'type' or 'metaphor' as in the case of these three days. There are various places in the Old Testament that give special meaning to three days. The gospels however only refer to the prophecy of Jonah. Christ said that Jonah would be the 'sign' that God would give the Jews, as a rebuke for their obstinacy. (Math 12:39-40). As Jonah was buried in a watery death for three days, then spit out and believed upon by Gentiles, so would Christ be buried in the belly of the earth and spit out miraculously to be believed on by the Romans and Greeks.
Beyond this single prophecy, there does seem to be more in the Bible and in rabbinic history that enshrines a three-day significance. The main idea seems to stem from Abraham arriving at Mount Moriah to sacrifice his son, on the third-day (Gen 22:4). This is another resurrection image no doubt. The idea is that Isaac was good for dead all three days until God provided a ram in his place. From this the third day, there seems to have become some concepts of a third day resurrection, further supported by Hosea 6:2. Notice though that Rabbi's often differed among themselves, just as we do with Revelation, so the three days in Hosea 6:2 was interpreted by some as 3000 years.
Despite the differing historical interpretations by the Rabbis, it cannot be denied that this three-day-theme existed before Christ. Still the bottom line is that in the New Testament Christ's reference to Jonah is enough to fully satisfy the statement that Chris was raised on the third day 'according to the scriptures' (I Cor 15:3-4) The Old Testament three day theme is mostly of supplemental interest.
For a deeper analysis on the three day theme, there is an excellent little article by Michael Brown at JewishRoots.net here.