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>given the expectation is defined not to change. To be clear, in a martingale the expectation is equal to the current value. It changes as the current value ch
by CrazyStat 4y ago
>given the expectation is defined not to change.
To be clear, in a martingale the expectation is equal to the current value. It changes as the current value changes (i.e. as time passes).
>Especially when the first example is often the stock market, and everyone knows you can't predict movements of the stock market...
Not being able to predict movements is exactly what "the expectation is equal to the current value" looks like. If you had information that changed your expectation to be different from the current value, that would be predicting a movement in one direction or the other.
- chinaman425 4y agoCome on, he meant accurately predict it, and you knew that.
- CrazyStat 4y agoYou appear to be shadowbanned. I vouched for this comment so that I could reply to it. If my expectation for a stock is something other than the current value, I am claiming that I can predict the price. It doesn't matter whether my predictions are accurate or not, it's a statement about my beliefs. A martingale model is consistent with believing that I can't predict the stock price. A non-martingale model implies believing that I can predict the stock price.