Ergodicity — an intuitive introduction

3 Apr, 2021 at 11:08 | Posted in Statistics & Econometrics | 6 Comments

Ergodicity is a difficult concept that many students of econom(etr)ics have problems with understanding. Trying to explain it, you often find yourself getting  lost in mathematical-statistical subtleties difficult for most students to grasp.

In the video below, Luca Dellanna has made an admirably simplified and pedagogical exposition of  what it means for probability structures of stationary processes and ensembles to be ergodic.

6 Comments

  1. After having seen this I wonder: Is ergodic simply the opposite of track dependent? Or is there some nuance I miss?

    • Sorry, of course path dependent is the correct word…

  2. Mr. Dellana mentions diversification as a strategy to avoid the dire predictions of ergodicists. Exchange-Traded Funds provide such ergodic advantages to individual investors.
    .
    Mr. Dellana also illustrates ergodicity using Russian Roulette. But he does not mention that financial innovation allows me to invest in the average (ergodic) returns of other Russian Roulette players without ever exposing myself to the risk of dying. Why doesn’t Dellana talk about those financial innovations? Finance has already solved the problems he highlights. Irreversibility does not apply to finance because central banks can step in to reverse losses without taking money from any taxpayer.
    .
    Ergodicists owe it to us to study financial innovations and adapt their models to fit the real world better …

    • Dellana mentions both of the financial techniques which you mention.
      At 20’20” into the video mentions the benefits of holding a large portfolio of diversified non-correlated assets.
      And at 19’30” into the video he explains how a company employing Russian roulette players is almost immune to the risks taken individuals.
      .
      Moreover, at 20’20″ Dellana indicates that a diversification strategy may fail if the risks are correlated, eg the systemic risks in 1929, 2008 etc.
      And at 6’25” and 14’15” into the video, he explains that there is no financial innovation which can ensure the survival of over-leveraged firms during recessions.

      • “And at 19’30” into the video he explains how a company employing Russian roulette players is almost immune to the risks taken individuals.”
        .
        Yes, but this is where the discussion should start: the company can sell an index of russian roulette to individual investors. Thus I can tie my time-series average to the ensemble average without risking death myself.
        .
        “Dellana mentions both of the financial techniques which you mention.
        At 20’20” into the video”
        .
        Why does it take twenty minutes, why not mention index funds, and why not emphasize that this financial innovation allows everyone to take advantage of ensemble ergodic averages to enhance their individual timelines?
        .
        “And at 6’25” and 14’15” into the video, he explains that there is no financial innovation which can ensure the survival of over-leveraged firms during recessions.”
        .
        This is wrong: Quantitative Easing ended both the 2008 and 2021 recessions in exponentially shorter time than the 1929 depression (which did not use the innovation of QE).
        .
        For a recent example, consider Melvin Capital, which would have gone bust due to over-leveraged short positions in Gamestop. However, a combination of regulations that had the effect of throttling GME demand, and a $2+ billion bailout from Citadel leaves Melvin Capital still an active player in financial markets.
        .
        Why not start the discussion with a model that describes actual financial bets in the real world? You have to discuss Exchange-Traded Funds and the options you can trade on them. The model of betting presented is archaic.

        • Then make your own video/book, if you think you can do it better. But, I hope you realize that not everyone shares your obsession with financialization of the economy


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