Disclaimer: I'm not well read in economics but am mathematically literate (PhD in Mech Eng)
Recently I was sent a paper from Nature Physics, "The ergodicity problem in economics" by Ole Peters.
I was discussing this with a friend who also isn't an economist but has more than just a passing interest.
He made the claim that in figure 2 of the paper the graph is wrong i.e. that the expectation values (the blue line) are wrong in that they should be plotting a plot of
0.9^(number of rounds/2), which would have a negative slope. He then goes on to say that this renders the paper garbage.
Now obvioulsy this paper was published in Nature Physics which currently has an impact factor of 22.8 so I find it hard to believe that this would have slipped past peer review.
So my question, is the paper wrong or is my friend?
One of the comments was where did the expectaion equation derive from. I'm not sure of my friends derivation but if you run the model proposed in equation 2 of the paper then you do indeed get an ever decreasng return. I used the following Python code to run the model...
from matplotlib import pyplot as plt import numpy as np wealth = 1000 num_tosses = 1000 h_t = np.random.randint(1, high=1000, size=num_tosses) x =  acc_wealth =  for idx, toss in enumerate(h_t): if toss % 2 == 0: wealth = wealth + (0.5*wealth) else: wealth = wealth - (0.4*wealth) x.append(idx) acc_wealth.append(wealth) fig = plt.figure() plt.plot(x, acc_wealth, "o-", lw = 2)
A typical plot of accumulated wealth v toss number....
This is clearly not what we're seeing in figure 2 of the paper...
Here the blue line is the accumulated wealth (log scale on the y axis) v toss number. It is increasing!!!
I'm going to post an amended version this on the Statistics Exchange page too.