Comments on: Martingales Don’t Do This

By: EL

EL — Tue, 23 Oct 2012 22:14:49 +0000

Or this:

http://www.theatlantic.com/business/archive/2012/10/should-presidential-campaigns-spend-more-money-manipulating-intrade/264000/

By: David Miller

David Miller — Thu, 18 Oct 2012 04:43:15 +0000

Rajiv: Now I get it; thanks! That was a great way to explain it. I still contend that one should not claim that Nate’s prediction is not a martingale without also claiming to have a superior model (I’m a Bayesian, not a frequentist), but your example illustrates that Nate’s model (or what we understand of it) seems to be at odds with what we know about how polls are conducted.

Jeff: Your suggestion to feed in past data to identify autocorrelations sounds like a pretty good tweak to the model, but it is rather frequentist, don’t you think?

By: jeff

jeff — Mon, 15 Oct 2012 15:40:35 +0000

right on rajiv.

By: Rajiv Sethi

Rajiv Sethi — Mon, 15 Oct 2012 12:07:01 +0000

Jeff, this is a really interesting post. The output of Nate’s algorithm can’t be interpreted as the probability of winning, despite the label on his graph. This is because his inputs are polls and economic fundamentals, and polls can be used to predict future polls (as Lones pointed out above). Specifically, when an event (such as the debate) causes a change in electoral prospects, it shows up first in the national tracking polls and the few state polls that happen to be in the field at the time. Over the next few days new states are polled and while each of the results contains noise, the average direction of movement is predictable. Nate’s model updates on these polls when they are released, ignoring the fact that part of the movement could have been predicted. They are treated as if they contain more new information than they really do.

In other words, the output of Nate’s model cannot be a martingale. In order for his graph to have the interpretation he claims for it, the model would have to forecast future polls and include these forecasts in his algorithm. I don’t believe he does this.

Intrade/IEM on the other hand, can include such information because traders are forecasting future polls. That doesn’t mean that prediction market prices are martingales, but at least it’s theoretically possible. For Nate’s series to be a martingale is theoretically impossible.

By: jeff

jeff — Mon, 15 Oct 2012 03:37:44 +0000

You will notice the perfect timing of my post. I was of course watching that trend and waiting until it was, predictably, done doing its trending, and then took the screenshot.

By: Alex F

Alex F — Mon, 15 Oct 2012 02:09:35 +0000

Jeff: Check 538 again today. I hope you didn’t lose any money betting that the linear trend would continue!

By: Tobias

Tobias — Sun, 14 Oct 2012 22:27:32 +0000

http://dilbert.com/strips/comic/2001-10-25/

By: David

David — Sun, 14 Oct 2012 03:42:04 +0000

This is a very interesting discussion for me. I can suggest two ways to explain the chart, and would be happy to hear your thoughts:
1. It is a martingale. The trend simply represents the specific martingale development – since the final value is close to the extreme usually, the uncertainty corresponds to events which could potentially happen until the election. each day there is some smaller chance of an important Event, and a bigger chance of nothing happening. When nothing happens the probability drifts (currently towards greater uncertainty it seems).
This is like an insurance martingale, the premiums accrue, and it looks predictable but the value process could be a martingale.
2. It could be that the 538 chart is a smoothed version of a spikier and closer to the intrade/IEM charts. Smoothing the IEM chart could make it look quite trend-like.

By: jeff

jeff — Sat, 13 Oct 2012 22:56:21 +0000

Ansh: the probability, conditioned on information at time t of an event to be realized at time T, viewed as a stochastic process, is a martingale.

If a prediction is intended to be interpreted as a probability then it must satisfy the laws of probability.

By: jeff

jeff — Sat, 13 Oct 2012 22:46:27 +0000

Sune: Good question. I think I mean something in-between. Suppose you take data from past elections and feed them into the model and ask whether there are predictable patterns. For example look to see whether there is autocorrelation in the increments.

The model should not be blind to the patterns that the model itself generates.