> If it's raining right now, it doesn't seem too far fetched to guess it will probably be raining in 1 minute.
That's a bit of an unfair example, though. If the Tesla stock is at 200 right now, the martingale property implies that I should expect it to be at 200 not just next minute or tomorrow, but also next week, two years from now, next decade, and so on. A martingale is not restricted in its time scale.
(This is using clearly expectation in the technical sense. The stock price may well go up, or go down, but we can't tell which or how much, so in the grand scheme of things, we're better off assuming it won't move at all.)
To expect a value of 200 means to have the average of 200 from this point in time onwards, assuming stock price is random walk. Not that the value tomorrow will be exactly 200. It could be 200, 201, 199, 202, 198 etc. the average expected is 200. If you possess no external knowledge such as insider information, then random walk is a sensible and obvious choice for stock price.
yeah there's a built in assumption that the behavior of the function we're estimating with martigale is continuous near the limit of the guess, and thus predictable over the interval of the guess and the prediction.
That's a bit of an unfair example, though. If the Tesla stock is at 200 right now, the martingale property implies that I should expect it to be at 200 not just next minute or tomorrow, but also next week, two years from now, next decade, and so on. A martingale is not restricted in its time scale.
(This is using clearly expectation in the technical sense. The stock price may well go up, or go down, but we can't tell which or how much, so in the grand scheme of things, we're better off assuming it won't move at all.)