How authentic is the Hadith that states: "Fasting a day from the ten days of Dhul-Hijjah is equivalent to a thousand good deeds, and more"?

No hadith has been reported that specifies the reward for fasting each day of the ten days. However, Al-Bayhaqi narrated an athar from Al-Hasan, from Anas ibn Malik, that "for every day of the ten days, there is a thousand [rewards], and the Day of Arafah is ten thousand days in virtue." Al-Hakim stated that it is not a marfu' hadith (a hadith directly attributed to the Prophet). As for the virtue of fasting in general, the Prophet, peace and blessings be upon him, said: "Every deed of the son of Adam is multiplied, a good deed by ten times its like, up to seven hundred times... except for fasting, for it is for Me, and I shall reward for it." The virtue of good deeds during the ten days has been confirmed by his saying, peace and blessings be upon him: "There are no days in which righteous deeds are more beloved to Allah than these days [the first ten days of Dhul-Hijjah]."