Gary Gorton, Harald Uhlig, and the Great Crisis

Gary Gorton has made clear that the financial crisis of 2007 was in essence a traditional banking panic, not unlike those of the ninetheeth century.  A key corollary is that the root cause of the Panic of 2007 can't be something relatively new, like "Too Big to Fail".  (See this.)  Lots of people blame residential mortgage-backed securities (RMBS's), but they're also too new.  Interestingly, in new work Juan Ospina and Harald Uhlig examine RBMS's directly.  Sure enough, and contrary to popular impression, they performed quite well through the crisis.

Dense Data for Long Memory

From the last post, you might think that efficient learning about low-frequency phenomena requires tall data. Certainly efficient estimation of trend, as stressed in the last post, does require tall data. But it turns out that efficient estimation of other aspects of low-frequency dynamics sometimes requires only dense data. In particular, consider a pure long memory, or "fractionally integrated", process, \( (1-L)^d x_t = \epsilon_t \), 0 < \( d \) < 1/2. (See, for example, this or this.) In a general \( I(d) \) process, \(d\) governs only low-frequency behavior (the rate of decay of long-lag autocorrelations toward zero, or equivalently, the rate of explosion of low-frequency spectra toward infinity), so tall data are needed for efficient estimation of \(d\). But in a pure long-memory process, one parameter (\(d\)) governs behavior at all frequencies, including arbitrarily low frequencies, due to the self-similarity ("scaling law") of pure long memory. Hence for pure long memory a short but dense sample can be as informative about \(d\) as a tall sample. (And pure long memory often appears to be a highly-accurate approximation to financial asset return volatilities, as for example in ABDL.)

Big Data for Volatility vs.Trend

Although largely uninformative for some purposes, dense data (high-frequency sampling) are highly informative for others.  The massive example of recent decades is volatility estimation.  The basic insight traces at least to Robert Merton's early work. Roughly put, as we sample returns arbitrarily finely, we can infer underlying volatility (quadratic variation) arbitrarily well.

So, what is it for which dense data are "largely uninformative"?  The massive example of recent decades is long-term trend.  Again roughly put and assuming linearity, long-term trend is effectively a line segment drawn between a sample's first and last observations, so for efficient estimation we need tall data (long calendar span), not dense data.

Assembling everything, for estimating yesterday's stock-market volatility you'd love to have yesterday's 1-minute intra-day returns, but for estimating the expected return on the stock market (the slope of a linear log-price trend) you'd much rather have 100 years of annual returns, despite the fact that a naive count would say that 1 day of 1-minute returns is a much "bigger" sample.

So different aspects of Big Data -- in this case dense vs. tall -- are of different value for different things.  Dense data promote accurate volatility estimation, and tall data promote accurate trend estimation.

StatPrize

Check out this new prize, http://statprize.org/ (Thanks, Dave Giles, for informing me via your tweet.) It should be USD 1 Million, ahead of the Nobel, as statistics is a key part (arguably the key part) of the foundation on which every science builds.

And obviously check out David Cox, the first winner. Every time I've given an Oxford econometrics seminar, he has shown up. It's humbling that he evidently thinks he might have something to learn from me. What an amazing scientist, and what an amazing gentleman.

And also obviously, the new StatPrize can't help but remind me of Ted Anderson's recent passing, not to mention the earlier but recent passings, for example, of Herman Wold, Edmond Mallinvaud, and Arnold Zellner. Wow -- sometimes the Stockholm gears just grind too slowly. Moving forward, StatPrize will presumably make such econometric recognition failures less likely.