I have heard somewhere that Jesus' past and future acts are symbolically mirrored in the Jewish feasts that the Lord commanded be observed in the old Testament. Do you know of any sources or anything more specific?

The seven annual feasts were spread over seven months, at set times appointed by God. They foreshadow the set times of God's work of redemption through His Son, Jesus as affecting both Jesus and believers in him.

THE PASSOVER
The term "passover" is to be considered in the sense of "hovering over", i.e. to protect or deliver. God's presence overshadowed His people for their protection. The nation of Israel was transferred from slavery until death in Egypt, to lifelong service to God. Likewise, the believer in Christ is delivered from bondage to sin, leading to death, to a life of service to Christ, leading to eternal life.

Jesus, the Lamb of God, is our Passover. 1 Corinthians 5:7-8, "For Christ, our Passover lamb, has been sacrificed. Therefore let us keep the Festival, not with the old yeast, the yeast of malice and wickedness, but with bread without yeast, the bread of sincerity and truth."

THE FEAST OF UNLEAVENED BREAD
This was a continuation of the Passover. Yeast (or leaven) promotes fermentation and Scripture uses yeast as a type of sin (1 Cor 5:6,7). Forgiveness for our sins can be obtained through the intercession of Christ, our mediator. Entry to this feast is possible only because "Christ our passover is sacrificed for us". Both the Passover and the feast without leaven show essentials for the believer. As there were 7 days eating bread without yeast, so for the believer there should be a complete life separate from sin. The sacrifice of Christ is of no benefit unless sinful yeast is excluded from our life.

THE FEAST OF FIRSTFRUITS
This prefigured the resurrection of Jesus. The ceremony took place on the third day from the Passover. Jesus rose the third day, 1 Cor 15:20, "Christ has indeed been raised from the dead, the firstfruits of those who have fallen asleep." Until the sheaf of the firstfruits had been presented to the Lord, no one was permitted to eat bread, parched corn, or green ears. So, until God had reaped the firstfruits from the tomb in the garden, there could be no gathering of the harvest. "But each in his own turn: Christ, the firstfruits; then, when he comes, those who belong to him." (1 Cor 15:23)

THE FEAST OF WEEKS (OR PENTECOST / HARVEST)
This was held at the beginning of wheat harvesting, seven weeks from the Feast of Firstfruits (Lev 23:15-16). In the New Testament it called Pentecost (Greek 'pente' = fifty) The festival commemorated the giving of the Law which took place 50 days after the Sabbath following the Passover. On the day of Pentecost following Jesus' resurrection, a new revelation was given to the people in the gospel preached by the apostles, with the invitation to all to enter a covenant with God through baptism into Christ (Acts 2:40).

THE FEAST OF TRUMPETS
Almost four months after the Pentecost, though not at a precise interval, the feast of Trumpets was a day of rest celebrated with trumpet blasts and sacrifices when the nation was presented before God. This prefigures the time when "the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God", 1 Thes 4:16 and, "in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed" 1 Cor 15:52.

THE DAY OF ATONEMENT
On this day the priests offered sacrifices of atonement for themselves and the people. This pointed forward to the work of redemption accomplished by Christ. In addition to personal atonement obtained through him, the scriptures refer to national atonement to be achieved at his second coming. Natural Israel will be humbled and then obtain national redemption, Isa 4:4. Then those nations that will be given a place in God's Kingdom will be gathered for the same purpose, Zeph 3:18.

THE FEAST OF TABERNACLES (OR BOOTHS / INGATHERING)
In contrast to the Day of Atonement, during which the Israelites were to afflict themselves, during this festival they are commanded to rejoice. This third great festival held at the end of the harvest prefigures the Millennium, when the redeemed shall rejoice before God, Rev 7:9-17. This feast will continue to be celebrated during the Millennium in anticipation of the final harvest to be gathered in by the Lord at the conclusion of the thousand years of peace. Zech 14:16. The harvest of faithful ones at the end of the Millennium will represent the final ingathering developed out of the waving of the first single sheaf (typifying the Lord Jesus Christ) on the first day of the week following Passover.

Should you wish to investigate the subject further, the following are suggested:

  • The Temple: Its Ministry and Services as they were at the time of Christ -- Alfred Edersheim
  • Thus Shalt Thou Serve -- C. W. Hemming