There are two types of odd people: odd knights and odd liars. Odd knights lie on odd-numbered days and tell the truth on even-numbered days. Odd liars tell the truth on odd-numbered days and lie on even-numbered days.

One day in either 2012 or 2013, an odd person made the following statements.

1. Today is either the 7th or the 8th.
2. Yesterday was the 31st.
3. I did not lie yesterday.

What type is the person, and what day did he/she say these statements?