If you look at their Table 6 (page 53), you can find their estimated date for the start of the recession: September 2000.
Menzie Chinn read the same paper and notes:
First let me make the observation that while Mankiw prefers the multivariate Markov Switching results in Table 6 of Hamilton-Chauvet, it is by no means the only set of estimates in the paper. Table 8, using the recursive estimation methodology indicates a March 2001 recession date – exactly the determination of the NBER Business Cycle Committee.
Menzie does a nice job of summarizing the paper co-authored by his co-blogger, but admits that we should ask Dr. Hamilton his view of to which methodology he finds more compelling.