Tuesday, November 11, 2008


Semi-technical definition:
In probability theory, a martingale is a stochastic process (i.e., a sequence of random variables) such that the conditional expected value of an observation at some time t, given all the observations up to some earlier time s, is equal to the observation at that earlier time s.
[Wikipedia, ]
A martingale forecasting model is very simple: Tomorrow will look like today.

What brings this to mind is this headline:
U.S. economy expected to contract in 2009
The article notes that, "The U.S. economy is expected to shrink 0.4% in 2009 compared with 2008, according to the monthly survey of 49 economists published Monday by Blue Chip Economic Indicators."

Yep - the economy went down yesterday, so the forecast is that it'll go down tomorrow.

Recall last spring and early summer, when oil was headed upwards of $140/bbl, the economic sages were suggesting that it could go as high as $200/bbl. (It's currently hovering around the low $60s/bbl.)

Numerous academic studies over the past 30+ years confirm that the best guess for tomorrow's stock price is today's stock price.

All economic forecasting based on anything more sophisticated than reading tea leaves or asking grandma is based on the assumption that "the future will look like the past." The differences between the myriad models out there is just which aspects of the past will be repeated, and just what constitutes the relevant past.

Recent economic projections (say, those made over the past year or so) all seem to suggest that "rate of change" is the dimension of past behavior most favored by forecasters, and that "yesterday" is the relevant past. That is, many - if not most - of the forecasts that have made the news in the past year seem to be based on a pretty simple model: the best guess for how tomorrow will look is based on assuming that the rate-of-change from today-to-tomorrow will be the same as the rate-of-change from yesterday-to-today. A martingale on rates-of-change.

Readers may notice a flaw in this methodology: it cannot predict a change in direction. As it turns out, there just aren't any good models in use that do a decent job guessing when 'up' will turn to 'down' or vice versa.
[Aside: a none-too-sophisticated analysis of recession frequency since WWII led me to predict (as part of my job as a forecaster) in Dec 2006 that there was better than an 80% chance of recession before 2010. When would it start? My none-too-sophisticated model didn't provide a guess.]

I believe I have just equipped my readers to forecast the economy at least as accurately as many of the high-paid economic gurus: tomorrow will look like today!

Aside: martingale forecasting is a purely statistical procedure, which takes into account nothing about economic 'fundamentals'. Economists like Krugman did a pretty good job suggesting more than a year ago that 'up' would soon turn to 'down' based on an analysis of these fundamentals.

... but most folks are happy to let their computer models do the thinking. And academic research over the past 30 years continues to affirm that, if you're letting your computer models do the work, the best model around is also the simplest: tomorrow will look like today.

Have a nice day.

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