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In this lecture, we are going to look at the code for the exponentially weighted moving average.

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As usual, 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 before we start to look at the code itself, let's talk about the data set in this lecture and for

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most of the lectures in this section, we'll be using the airline passengers data said.

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This is a famous time series analysis data set, and it's basically the mists of Time series analysis.

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That said, the first line here is to download our airline passengers CSFI.

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Next, we import pendas and non-pay, not too surprising.

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Next, we use prediabetes, D.V. to load in our CSFI.

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Again, not too surprising.

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Notice that the indexed column is month.

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So this is monthly data rather than daily data.

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Next, we do a different head to see the first few rows of our data set.

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As you can see, our index is the month and the passengers column contains the number of passengers

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in that month.

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Next, we do advocate is in L.A. to check if there are any missing values.

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Since the summer zero, there are no missing values.

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Next, we do a plot to plot our data said.

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So let's spend some time analyzing what we are seeing, first of all, this looks nothing like a typical

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stock price time series.

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There seems to be very little randomness in this data set.

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In fact, that would mean that this is a great candidate for statistical in machine learning techniques.

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Remember that we used to call machine learning pattern recognition.

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That is, machine learning is all about recognizing and modeling patterns.

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And clearly there is a pattern here.

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On the other hand, stock prices might be characterized by their lack of patterns.

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We can see that with this data set, there seems to be a trend component and the cyclical component

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of the trend means that the signal is generally going upwards.

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The cyclical component means that there's some periodicity where the same pattern repeats itself.

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We can see that this cyclical pattern actually amplifies over time, so it's not a constant cyclical

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pattern.

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It's also difficult to tell whether the trend is increasing linearly or if that is also increasing over

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time, perhaps exponentially in this Time series.

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We don't have enough data to see that.

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However, one might surmise that many real world phenomena grow exponentially.

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For example, the number of transistors on an integrated circuit grows exponentially.

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This is known as Moore's Law due to recent world events.

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We know that viral transmission exhibits exponential growth.

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Of course, this is limited at some point since the world population is finite.

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So in fact, the overall curve might look like a sigmoid.

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Let's begin by setting our alpha parameter to zero point two.

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Why did I choose a zero point to no particular reason you can think of this as a hyper parameter that

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you can optimize?

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Next, let's calculate the WEMA, this can be accomplished by first using the IWM function we pass in

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our alpha parameter and we say adjust equals false y adjust equals false.

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When you set adjust equals true, it actually does a different calculation than what we discussed in

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the three lectures, which is not what one usually considers to be the WEMA.

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So we use adjust equals false so that Pendas uses the method we expect.

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Finally, we call the mean function because we want the exponentially weighted moving average, which

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corresponds to the exponentially weighted mean.

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We assign the result to the column called a.

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Next, just in case you're interested in the data type returned by the EWTN function, I've printed

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that out.

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So as you can see, we get back an object of type IWM, so if you're interested in looking at the documentation

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for this object now, you know which page to go to.

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Next, we do a plot to plot everything currently in our data frame, as you can see, the exponentially

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weighted moving average is kind of like a delayed and adaptive version of the original data set similar

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to the simple moving average.

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You might want to play around with the value of Alpha to get a better feel for how it affects the moving

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average.

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Next, what I always like to do if the equation is simple enough, is to check whether Pendas is doing

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what we expect it to do.

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That is, does it implement the formula we discussed in the theory lecture to check this?

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We're going to use that formula manually to start.

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We're going to create an empty list called Manual WEMA.

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Next, we're going to look through every element in the passenger's column of our data set inside the

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loop.

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We're going to check whether our manual GWM list is empty or not.

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Remember that the IWM is calculated based on its previous value.

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If there is no previous value, then we can't use the formula.

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Of course, that occurs on the very first value.

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The question is how does it WMA initialize itself?

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In fact, there are many answers to this question you may have seen in my machine learning course is

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that the typical answer is to set the first value to zero.

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This induces a bias in the moving average because if, let's say all your actual values are above one

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hundred, as they are in this case, the average is going to get pushed down from one hundred to zero

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as if zero were actually part of the data set.

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There is a way to correct this using a method called bias correction, which is used in modern optimization

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algorithms such as Atem.

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However, that's outside the scope of this course for us.

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We will simply use the method of copying the first value.

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Otherwise, when the length of manual WMA is greater than zero, we simply use our formula.

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We assign the result to X hat and then we append X had to our list.

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Finally, when we are outside this loop, we assign our list to a new column of the data frame called

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Emmanuel.

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Next, we do a doughnut plot again.

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We see that, indeed, our manual calculation appears to match what Panis does.

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Now you have a much better understanding of what Panis is doing under the hood.

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Not that we can also do a detached head to check how close the values actually are from the small print

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out, they appear to be exactly the same.

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Now, since these two columns are exactly the same, the next thing I'm going to do is remove the manual

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column since it's redundant.

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This will help us clean up our data frame for the next few lectures.