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17 comments
Comments feed for this article
October 13, 2012 at 2:45 pm
David Miller
Why not?
October 13, 2012 at 4:14 pm
jeff
You could have predicted that the linear trend would continue.
October 13, 2012 at 5:09 pm
Sune Kristian Jakobsen
When you say “You could have predicted that the linear trend would continue” do you mean based only on the graph with the last couple of days missing, or are you only saying that someone who follows American politics would have predicted that it continued? The later does not contradict the claim that the prediction is a martingale, it is only saying that the prediction does not take all the available information onto account. And I don’t see a reason at someone looking a the graph a few days ago without knowing what is was, should have predicted that the decline continued. Would they say the same today? And in mid September?
October 13, 2012 at 5:19 pm
Ansh
@ Jeff… what? Firstly, there is no reason why predictions ought to be martingales. We only know that market prices must be discounted martingales. Secondly, if those were market prices of some kind, there is not reason why a particular price path can’t look like anything at all. Also, maybe *you* could’ve predicted the downward trend, but clearly those who bought the security didn’t think it was going downwards.
October 13, 2012 at 5:46 pm
jeff
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.
October 13, 2012 at 5:56 pm
jeff
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.
October 13, 2012 at 3:55 pm
o
Nor this:
http://iemweb.biz.uiowa.edu/graphs/graph_Pres12_WTA.cfm
October 13, 2012 at 4:18 pm
jeff
That picture has a few big jumps and a lot of bouncing around. The 538 has one constant predictable decline.
October 13, 2012 at 4:46 pm
Lones Smith
I know these are Intrade odds, but I fear that the investors here do not realize that election polls are not martingales. See my paper on election timing. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=900460
October 13, 2012 at 10:42 pm
David
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.
October 14, 2012 at 5:27 pm
Tobias
http://dilbert.com/strips/comic/2001-10-25/
October 14, 2012 at 9:09 pm
Alex F
Jeff: Check 538 again today. I hope you didn’t lose any money betting that the linear trend would continue!
October 14, 2012 at 10:37 pm
jeff
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.
October 15, 2012 at 7:07 am
Rajiv Sethi
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.
October 15, 2012 at 10:40 am
jeff
right on rajiv.
October 17, 2012 at 11:43 pm
David Miller
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?
October 23, 2012 at 5:14 pm
EL
Or this:
http://www.theatlantic.com/business/archive/2012/10/should-presidential-campaigns-spend-more-money-manipulating-intrade/264000/