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In this lecture, we are going to look at how to work with the simple moving average in code.

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This lecture is going to walk you through a Prepare to CoLab notebook.

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Although a very good exercise, which I always recommend, is once you know how this is done, to try

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and recreate it yourself with as few references as possible.

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As always, you can check the lectures, how to code by yourself and how to practice for a more in-depth

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discussion.

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If there's anything in this lecture you didn't understand or you think I missed the step or didn't explain

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why we were doing something, please use the Q&A to inquire.

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As always, you can look at the title of the notebook to determine what notebook we are currently looking

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at.

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So let's start by downloading the file esp five closed at CSC.

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As you recall, this is our CSC of Close Presses Only.

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Next, we're going to import our usual libraries, pandas, map, plot, lib and numpy.

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Next we read in the csv as a dataframe using PD to read CC.

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Next we grab the clothes prices for Google since we're going to drop the end values.

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We want to make a copy first.

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Will assign this to the variable goog x.

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We'll do a google dot head as a sanity check to see what's in our data frame.

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Next, we'll do a Google plot to see Google stock prices as a time series.

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Next we'll calculate the log returns for Google by calling the percent change function, adding one

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and then taking the log.

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Next, we plot the log returns as a time series.

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Next, we're going to test our moving average and code.

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So on the right side, you'll see that I'm going to grab the GOOG column.

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Then I call the rolling function passing in ten for the window size.

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Then I call the mean function to say that I want the rolling mean.

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Finally, I assign this to a new column called Smart ten.

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Next we call the head function, with the argument 20 to say that we want to see the first 20 rows of

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our new data frame.

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As you can see, the first nine rows of semi ten are nine.

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This is because no rolling window of size ten exists for these elements.

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We can see that the first value in, say, May ten shows up in the 10th row as expected.

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You might want to do a manual test calculation to ensure that these values are what you expect.

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That is, calculate these values by hand.

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Next I do another little sanity check to see what type of object is returned by the rolling function.

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As you can see, it's an object of type rolling.

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This is always useful in case you need to look up the documentation, you know exactly which page to

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go to.

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Next I call Google Plot again so that we can see our new column plotted against the original Time series.

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She?

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As you can see, it's basically a smoother version of our original Time series.

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You might want to zoom in on your own computer or just select a few rows to see this more clearly.

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Next, we're going to calculate another a simple moving average, but this time with a window size of

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50.

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As you can see, this is the exact same code as before, except with 50 instead of ten.

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When we plot this, we see something very interesting.

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First, smart 50.

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By using more values in its sample, mean is even smoother than, say, ten.

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So your lesson is that the more values you use, the smoother the resulting time series will be.

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Second, you will see this lagging characteristic in the Time series.

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That is, it appears as if the simple moving average lags behind the original TIME series.

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If you try different window sizes, you'll see that this effect becomes more and more pronounced as

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the window size gets larger and larger.

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Next, we're going to work with a Multidimensional Time series.

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Let's create a new data frame by using both Google and Apple stocks.

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Again, we make a copy and drop any any values.

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We'll call this data frame goog aapl.

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On the next line.

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You can see that after calling the rolling function, I have other options than just the mean.

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Since we now have two columns of data, I can calculate the covariance.

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As you can see, the results of this is pretty strange.

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On the left hand side of this data frame, we can see a sort of multilevel index.

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At the top level is just the date, but there's a sub level where we get to choose either Apple or Google.

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So if you were to index this data frame by date, you would get a two by two covariance matrix.

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This is kind of a weird way of storing what is really a three dimensional tensor and a two dimensional

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data frame.

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Next, I demonstrate how you can select a single row by date and convert it to an empire way to get

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a single covariance matrix.

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Now, as you know, in finance, we like to work with returns rather than prices.

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So in the next block, we're going to calculate the log returns for both Apple and Google.

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Notice that this is exactly the same code as before.

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Since it works for one or multiple columns.

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In the next block, we're going to calculate the simple moving average for both Apple and Google returns.

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Notice that again it's just the same code as before.

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Excepts repeated twice.

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Next, we plot both Googles and Apples returns along with their moving averages.

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It's interesting that there seems to be a pretty strong correlation between their returns, although

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there are definitely some outliers.

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Recall that we discovered this in an earlier lecture as well.

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Next we calculate the rolling covariance of the returns.

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To do this, we call rolling 50 and then we call the code function.

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If we do a cocktail, we can see the last few rows of the covariance data frame.

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Notice that if I don't pass in any arguments into the tail function, it just prints out the last five

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rows, which cuts off one of the covariance matrices.

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So this is a full covariance matrix.

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This is a full covariance matrix.

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And this is half of one.

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Next we calculate the rolling correlation of the log returns.

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To do this, we call rolling 50 again and then we call the core function.

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If we do a core detail, we can see the last few rows of the dataframe I've passed in 16, so that we

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see the last eight correlation matrices in full.

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Notice how the correlation matrix changes over time?

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For most of the correlation matrices, we can see that there is a negative correlation between Apple

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and Google returns, at least for these time periods.

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The final correlation is positive, demonstrating that the correlation can even change direction.