Detecting and forecasting business cycle turning points

The R word has begun to appear in the media again bringing with it three technical questions viz, How will we know we are in recession? How will we know when it has ended? And How can we forecast its onset and ending? This paper does not provide answers to these questions rather it focuses on the technical issues that we need to resolve in order to provide good answers to these questions. The paper has three significant findings. First, the business cycle states obtained by the BBQ algorithm are complex statistical processes and it is not possible to write down an exact likelihood function for them. Second, for the classical and acceleration cycles it is possible to obtain a reasonably simple approximation to the BBQ algorithm that may permit one to write down a likelihood function. Third, when evaluating these algorithms there is a large di¤erence between the results using US GDP as compared to UK GDP or simulated data from models fit to US GDP. Specifically, turning points are much easier to detect in US GDP than in other series. One needs to take this into account when using US based research on detecting and forecasting business cycle turning points.