When we commonly speak of the "Jewish holidays," we are referring to the biblical holidays, which are summarized in Leviticus chapter 23. There can be little doubt that Jesus, like any other Jewish person of his time, must have kept all the biblical holidays. If He had not observed the Jewish holidays, He would have set himself apart from his community, and we know that this was not the case.
We know for sure that He attended synagogue because is recorded in the gospels. In Mark 6, it says that that when the Sabbath came He went to the synagogue and there He addressed the people. There is also the case of Jesus healing a man while He was at the synagogue.
Another clear indication that Jesus observed the biblical holidays is the fact that all four gospels record His last Passover. Jesus celebrated Passover to the fullest, making sure that all elements of the celebration were fulfilled and sending His disciples ahead of time to make things ready for the Passover meal.
In the Old Testament, the Lord commands the people of Israel to observe these celebrations throughout all generations, His "appointed times" are part of His covenant with the people of Israel. In other words, the observance of the biblical holidays was a unique distinction and a commitment of the Jewish people that set them apart from the rest of the nations. If Jesus had not observed the biblical holidays, the gospels surely would have indicated this, because it would have been highly irregular for a Jewish person of that time.
Moreover, it is my firm conviction that the disciples as well as the early church continued observing and celebrating the biblical holidays because they recognized that these Holy Days are fulfilled in the life and ministry of Jesus. Regrettably, after two centuries of church history, when the number of Jewish believers was surpassed by Gentile believers, the church stopped celebrating the biblical holidays and began to "de-Judaize" Jesus, the very founder of the church.