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OK so that's lesson number one.

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The lesson is that it's actually very unconventional to try and predict the stock price in the first

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place.

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Instead what we really want to try and predict is the stock return.

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The return is defined as follows for a given period of time.

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The return is the final price minus the initial price divided by the initial price

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not just for some intuition.

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This is the same formula you would use when you want to calculate a sale.

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So for example what does it mean when we say something is 20 percent off intuitively you know that if

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something costs 100 dollars and it's 20 percent off then you'll pay 80 dollars.

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But we can also calculate this another way.

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Take 80 subtract one hundred and divide by one hundred.

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That's minus 20 percent.

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In other words the price you pay is 20 percent less than the original price.

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So to summarize when financial engineers do quote unquote stock prediction they are usually looking

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at some form of return not actual prices.

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OK so back to the code since we're working with a pan this data frame this is somewhat convenient at

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least if you know the right functions to call

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as usual we want to process our data in a vector rise form meaning we do some operation on all the columns

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at once.

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So first we need to shift at the closing price up by 1 so that yesterday's closing price is aligned

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with today's closing price.

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So x of 2 is beside x of 1 as a 3 is besides 2 and so on.

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Then we can subtract them all in one step so let's do DFT it had to look at the result now as you can

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see the first row is in again because we don't know the previous price for that row since it's not in

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our dataset.

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This is not a problem for us because we are building an hour in n it's going to take the first 10 days

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of data to predict that the eleventh day.

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So that would be from here up to the tenth row.

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So we never even use this value.

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All right so the 11th row is much further away than the first row.

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So if the first row has any ends as long as you're not in the target that's fine.

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Next we do our return calculation.

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So we say D F return is equal at the close minus the F previous close divided by the previous close.

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Let's do it.

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The FDR had again to look at these returns.

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So again the first value is in n n.

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But we don't care

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next we do a plot of this time series.

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Conceptually this is no different from the stock price or a sine wave.

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It's still just a time series but as you're beginning to see sometimes series are harder to learn from

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than others.

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Next we draw a histogram so we can see the distribution of returns we can see that these are pretty

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small values.

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So we might want to normalize them so we're going to go through the same thing again where we assign

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the returns to a variable called series as an end by one matrix.

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Note that here I'm taking dot values at index 1 and up because the 0 with index is an N N as before

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we create a standard scalar call fit on the first half and call it transform on the whole thing and

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then flatten it back to an N length vector.

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Next we're going to go through all the same steps to build our supervised learning dataset and train

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our auto regressive on and model this code again isn't any different than the previous code.

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It's only the data itself that's different in now we are working with the series as the return rather

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than the actual stock price.

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So here's the data his are and then model and here's the result of training so the loss starts out at

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about 1

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and then by the end of training the loss is about point 8 7 and the test loss is about one point five.

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So it's pretty clearly over fitting

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well we can see from this is that the model has a much harder time learning anything.

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If we look at the loss per iteration it looks like the loss goes down a tiny bit but only at the cost

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of the validation loss going up.

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In other words it's just fitting to the noise.

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Next we're going to do a one that forecast

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and so here are the results.

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Now it's hard to tell whether this is good or not but judging by the previous loss values it's probably

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not good as an exercise.

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You might want to try to run this locally so that you can zoom into the plot and check for yourself.

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Next we're going to do a multi-step forecast.

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So here are the results for the multi-step

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so again we have the situation where the model doesn't really match up that well with the actual time

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series.