# Comparing Two Mountains, from Victor Niederhoffer

October 19, 2011 |

Dear Steve,

Hope you are well. A statistical problem has come up. The idea of comparing two charts, in this case Netflix and Green Mountain Coffee. I wonder if statisticians have a way of handling this problem. I've seen some books on statistics on place but never this problem of comparing two mountains as to their similarities. I wonder if you could refer me to the proper area. I asked a geologist whether they have a way, and apparently they take into consideration many physical factors. I am going to enclose the chart separately.

## Stephen Stigler replies:

Hi Vic,

Any statistical model would have to have a dynamical model for the mountain. It could be an empirical model, like if you had a sequence of mountains, as with predicting sunspot cycles or tides. But it would either need a number of examples (not just two) or a very strong math hypothesis. You might be able to generate a set of examples if you focus on a telling feature, like one day descent of x% after trading within + or - y% for z days.

Hope all is well with you & yours!

Best,

Steve

## Pitt Maner comments:

A geomorphologist would have to consider many factors in trying to interpret how the hills and valleys were formed, the timing of such, and what they might look like in the future. Erosion is a key but it can occur at differing rates within a range of timescales based on rainfall, climate, vegetation, composition and homogeniety of the rocks, fractures, landslides, river sediment carrying capacities and as noted in the article below—Slope . There are instances, however, where the rate of erosion at the surface is offset by the continuing forces of uplift (denudational isostatic rebound for word lovers).

There are rules of thumb— with the higher slopes and steep mountain ridges eroding quite quickly —E. Himalayas at a whopping 2 to 3 mm/yr, as example.  But those erosional rates will change over time to meet new equilibrium requiremen ts.

"I don't think we'll ever find the single smoking gun of erosion," says Portenga, "the natural world is so complex and there are so many factors that contribute to how landscapes change over time. But as this method develops, we will have a better sense of what variables are important — and which are not — in this erosion story."

For example, it has been a truism of geology for decades that rainfall is the biggest driver of erosion. Semi-arid landscapes with little vegetation and occasional major storms were understood to have the greatest rates of erosion. But this study challenges that idea. "It turns out that the greatest control on erosion is not mean annual precipitation," says Bierman. Instead, look at slope.

"People had always thought slope was important," Beirman says, "but these data show that slope is really important."

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