The book Hosea was written by the prophet Hosea.

Scriptures quoted by other authors

Matthew quoting Hosea

And he (Joseph) rose and took the child (Jesus) and his mother by night and departed to Egypt and remained there until the death of Herod. This was to fulfill what the Lord had spoken by the prophet,

“Out of Egypt I called My son.”

-- Matthew 2:14-15 (ESV)

However, Hosea did not prophecy about Jesus. Instead, he referred to Israel:

When Israel was a child, I loved him,
And out of Egypt I called My son.
As they called them, so they went from them;
They sacrificed to the Baals, and burned incense to carved images.

-- Hosea 11:1 (ESV)

It does not make sense that Jesus would "sacrifice to the Baals" or "burn incense to carved images". What Matthew perhaps tried to communicate is that Jesus had a similar experience like the Israelites that had to come out of Egypt after God dealt with the king.