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I have observed the historical PE (price / profit) value of a stock and realized that it roughly follows a log normal distribution. However, even when the next earning data point is easily predictable, this distribution cannot be used to predict the distribution of next stock price data point, because, the next PE value depends on the previous one, thus it is not set of repeated independent trials. In other words, for a regular random variable that follows the log normal distribution, the next value can be anything, regardless of the current value. But for the PE value of a stock, it must change gradually.

It is also not exactly a random walk, because for the random walk, the next step's direction is also independent of the previous step. This is not true for the PE, when it is too low, it is much more likely to go up than go down.

So my question is, what kind of random process can properly model the movement of the PE, which changes gradually, but overall, follows a log normal distribution?

gung - Reinstate Monica
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Sam
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  • You may be interested in reading this thread: [What machine-learning algorithm can be used to predict the stock market?](http://stats.stackexchange.com/questions/21395/) – gung - Reinstate Monica Dec 18 '12 at 03:21

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Try the following:

  1. Take the log of the PE ratios.

  2. Apply a time series model that you already have the software for. For example ARIMA, ETS.

  3. Exponentiate the forecasts. Do they look realistic?

  4. Repeat the above three steps to test your model out of sample.

Disclaimer: Earnings are announced at sparse intervals. There are others factors that are not being measured with the above suggested procedure.

power
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