Thomas wrote:georgeob1 wrote:Surely one as well versed in physics and economics as you understands the problems attendant to discrete sampling of continuous variables and the aliasing and other distortions that can result. They are indeed dependent on the sampling interval, despite your assertion to the contrary.
That wasn't my point. I'm not disputing that it depends on the sampling in principle. I'm disputing that this makes a big difference in practice. Nyquist's sampling theorem tells us that when you sample a continuous function in discrete intervals, you can reconstruct the function from the samples with a precision of twice the sampling interval. Almost all recessions, and certainly all business cycles, last longer than twice any sampling interval the BEA might realistically use.
At the risk of disappointing you, George, I think your talk about sampling intervals is a big red herring. The BEA's definition of recessions is sound.
In the first place I wasn't arguing about the quality of any definition - except the one Cicerone quoted and posted here. He left out the minimum interval from the definition, and those who were arguing the point were indeed talking past each other precisely because of the omission of any stated or even implied minimum interval.
As a related matter your description of Nyquist's theorem is deficient and misses the point in question.
"Aliasing" (the term I am accustomed to use) simply means that any reconstruction of a continuous variable from discrete sampling will provide an accurate representation of the underlying function only on intervals larger than twice the sampling interval. Another equivalent statement is that one must discretely represent twice as many wave numbers as are accurately represented in the approximated function. In practical terms this means that the threshold of our ability to detect the onset of a recession occurs no sooner than twice the sampling interval after the supposed new phase is presumed to have begun. If the economic statistics are based on quarterly samples then they can be used to accurately indicate a new trend only after two quarters of it have passed -- similarly for monthly or other intervals. This too was directly relevant to the (largely useless) discussion.
In addition for non-linear functions there are a host of other forms of aliasing that can have large qualitative effects on any approximation. The real operation of the economy, as well as the approximate mathematical models used to represent it, are highly non-linear. Hence my observation that recessions and other like economic "phases" are identifiable and useful mostly in retrospect.