How well can business cycle accounting account for business cycles?

The business cycle accounting method introduced by Chari, Kehoe and McGrattan (2007) is a useful tool to decompose business cycle fluctuations into their contributing factors. However, the model estimated by the maximum likelihood method cannot replicate business cycle moments computed from data. Moment-based estimation might be an attractive alternative if the purpose of the research is to study business cycle properties such as volatility, persistence and cross-correlation of variables instead of a specific business cycle episode.