The two periods are a bit of a mystery because the passage does not tell us when either the 390 years or the 40 years began, and we are not told anywhere else in Scripture either. Ezekiel was instructed to start giving this dramatic lesson to the exiles in the fifth year of Jehoiachin’s captivity. Jehoiachin, and Ezekiel, went into captivity in 598 bc, so the fifth year was 594 bc.
The beginning and end of the 390 years for the northern kingdom of Israel
The 390 years possibly began with the rebellion of the northern tribes under Jeroboam in the reign of Rehoboam. This would be a fitting start for the time of sin by the northern tribes (which after the split from the royal house of Judah were called Israel).
Solomon reigned from 971 to 931 bc. Jeroboam did not lead the northern tribes to rebel from the royal dynasty of David until the third year of the reign of Rehoboam (2 Chron 11:17) in 928 bc.
390 years after 928 bc was 538 bc. Babylon fell to the Persian king Cyrus in the early hours of 13th October 539 bc. And Cyrus made a decree that the people could go back to Jerusalem and rebuild the temple in his first year. Though Cyrus had ruled Persia since 559 bc the first year of his rule in Scripture is dated from his conquest of Babylon in 539. The Persians used accession year dating, so Cyrus’s first year would then be dated to 538 bc. 928 to 538 bc would be the 390 years relating to Israel.
If this is the correct interpretation then the years would include not only Israel’s years of apostasy against God but also the years of captivity in Babylon which were God’s response, his judgement, to their apostasy. So the 390 years are essentially all the years of separation between God and the northern tribes of Israel as a consequence of their sin.
The 40 years for the southern kingdom of Judah
If finding a suitable 390 year period was difficult for the northern tribes, then finding a suitable 40 year period for Judah is even more difficult. It also implies that the kingdom of Judah is nearly ten times less guilty than the northern tribes, which might not be the intention of the lesson.
Such is the difficulty of finding a suitable 40 year period that it is mostly considered as a period symbolizing God’s judgement prior to restoration. So the first period of forty in scripture was at the Flood: it rained forty days and forty nights (Gen 7:12) in judgment for the sin of the human race, but afterwards there was restoration. And the Israelites were forty years in the wilderness because of their sinful unbelief and rebellion (Numbers 14:33-34), but afterwards they were restored to God’s favour and entered into the Promised Land.
Secondly the 390 years plus 40 years makes a period of 430 years. This was the time the Israelites “suffered” in the land of Egypt (Exodus 12:40), but afterwards they were delivered and restored to favour in the Promised Land.
This interpretation I have taken from Frank W. Hardy at historicism.org which I have so far found the most likely. Frank Hardy is/was, like the eminent Bible chronologist Edwin Thiele, a Seventh Day Adventist. There are a few interpretations on the internet which I consider are plainly wrong because they have the wrong years for major Old Testament events. Frank Hardy uses dates which I believe are both accurate and finally settled.
Ezekiel’s drama lesson is emphasising:
The exile is because of so many years of sin, if you had not sinned there would be no exile;
By the time of the start of the Babylonian supremacy, starting 609 bc, the northern tribes had effectively ceased to exist. Many of the Israelites had gone into captivity in the days of the Assyrian Empire in 722 bc and been taken to live in other parts of the Assyrian Empire: and they had been replaced by peoples from other regions (2 Kings 17). But what the drama of Ezekiel is saying is that if there are any descendants of the northern tribes which can prove their descent then they are still the covenant people of God. They still have a claim to the special covenant relationship.
God is saying to his people: These years of exile are preparatory to a wonderful restoration of the covenant relationship with God. It must not be assumed that all is lost, that God has given up on his covenant people.
Assuming the above interpretation is correct then in addition to these lessons we have, by Ezekiel’s drama, evidence that the beginning of the reign of Darius the Mede over Babylon is precisely the same year as the beginning of the reign of Cyrus as King of the whole Empire. The reign of Cyrus did not follow on from a short reign of Darius the Mede: it seems Darius the Mede was appointed as king of the province of Babylon by Cyrus the Great. This is what is suggested by Daniel 9:1 where we read that Darius the Mede “was made king”. The province of Babylon was too significant a region to be ruled by someone merely called a “governor”… the title “king” was the more appropriate title.