A Day, but NO Atonement
if you don't have the Messiah
Lev. 23:26] And the LORD spake unto Moses, saying,27: Also on the "tenth day" of this "seventh month" there shall be a day of atonement: it shall be an holy convocation unto you; and ye shall afflict your souls, and offer an offering made by fire unto the LORD.  And ye shall do no work in that same day: for it is a day of atonement, to make an atonement for you before the LORD your God. For whatsoever soul it be that shall not be afflicted in that same day, he shall be cut off from among his people. And whatsoever soul it be that doeth any work in that same day, the same soul will I destroy from among his people. Ye shall do no manner of work: it shall be a statute for ever throughout your generations in all your dwellings. It shall be unto you a sabbath of rest, and ye shall afflict your souls: in the ninth day of the month at even, from even unto even, shall ye celebrate your sabbath.
Num. 29: And ye shall have on the tenth day of this seventh month an holy
convocation; and ye shall afflict your souls: ye shall not do any work therein:
 But ye shall offer a burnt offering unto the LORD for a sweet savour; one young bullock, one ram, and seven lambs of the first year; they shall be unto you without blemish:
 And their meat offering shall be of flour mingled with oil, three tenth deals to a bullock, and two tenth deals to one ram,
 A several tenth deal for one lamb, throughout the seven lambs:
 One kid of the goats for a sin offering; beside the sin offering of atonement, and the continual burnt offering, and the meat offering of it, and their drink offerings.
1Kgs.8:2 And all the men of Israel assembled themselves unto king Solomon at the feast in the month Ethanim, which is the seventh month.
The word afflict in Hebrew is "anah" meaning abase, humble or repent and never as "fast" in the scriptures. The Hebrew word "tzum" means fast and is "Never" used in connection with the Day of Atonement. Rabbinical Judaism has tried to replace "the Blood Sacrifice" with fasting.
Lev.17  For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.
Read Lev.16: 1 to 34
The Blood of the sacrifice was to be the most important feature of the biblical Day of Atonement. NOTHING can change this! Nothing can be a substitute for the obligatory sacrifice the Law of Moses demands and without which there can be no atonement.
Jer.14 When they fast, I will not hear their cry...
Since the Temple was destroyed and the priesthood abolished, a proper Day of Atonement has been impossible to keep.
To whom shall we go?
Within a few years after Messiah's death on the tree and His Resurrection God permitted the Temple tp be destroyed and the priesthood abolished. It had served it's purpose and was no longer needed. The temple and priesthood are "shadows of things to come". They "point" to the Messiah, the Great Hight Priest and the perfect Lamb of God, without blemish, who took away the sins of the world when He shed His Blood on the tree.
There is only one way to know God and enjoy peace with Him through the forgiveness of sins, and that is believing in Yeshua the Messiah Whom the biblical Day of Atonement "typified" and pointed to. As the scriptures below say:
Heb.9 Now when these things were thus ordained, the priests went always into the first tabernacle, accomplishing the service of God. But into the second went the high priest alone once every year, not without blood, which he offered for himself, and for the errors of the people: The Holy Ghost this signifying, that the way into the holiest of all was not yet made manifest, while as the first tabernacle was yet standing: Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience; Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation. But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building; Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us. For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance. For where a testament is, there must also of necessity be the death of the testator. For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth. Whereupon neither the first testament was dedicated without blood. For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people, Saying, This is the blood of the testament which God hath enjoined unto you. Moreover he sprinkled with blood both the tabernacle, and all the vessels of the ministry. And almost all things are by the law purged with blood; and without shedding of blood is no remission.
 It was therefore necessary that the patterns of things in the heavens should be purified
with these; but the heavenly things themselves with better sacrifices than these. For
Messiah,Christ is not entered into the holy places made with hands, which are the figures of the
true; but into heaven itself, now to appear in the presence of God for us: Nor yet that he
should offer himself often, as the high priest entereth into the holy place every year with blood of
others; For then must he often have suffered since the foundation of the world: but now
once in the end of the world hath he appeared to put away sin by the sacrifice
of himself. And as it is appointed unto men once to die, but after this the judgment:
 So Messiah,Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation.