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OK, so in this lecture, we are going to discuss Etes for Beginners.

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This is the lecture you should watch to gain some intuition behind the techniques in this section,

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but you don't necessarily care about how or why it works.

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So to recap what we said in the intro, the basic premise of this section is the moving average.

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The moving average is a simple concept.

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You take a window and slide it across the time series.

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And at each point in the Time series, you take the average of all the numbers in that window.

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That's called the simple moving average in pendas.

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You can do this in just one line of code.

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Now, you might think that this is too simplistic for the real world, but in fact, this simple concept

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is used for algorithmic trading, for presenting covid counts to the public and so forth.

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Now, the simple moving average is, in fact, a bit too simple, one way to view it is it's equally

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weighted since each point you, including your average, matters the same amount.

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Basically, if you have end points, then each point gets a weight of one over end.

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In contrast, we also have the exponentially weighted moving average, which weights each point exponentially

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going back in time.

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So in this case, we don't have a sliding window, but instead all past data points count.

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Going back to the start of your Time series.

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The intuition behind this is it's saying Newar points matter more than older points, so they get higher

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weights.

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But essentially the effect is the same for both the ESMAY and the WEMA.

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The output looks like a smoothed out version of the input.

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That's the meat tends to lag a bit more, but they both basically do the same thing.

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So how can we use the exponentially weighted moving average to actually build a forecasting model?

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Well, the simplest method is called a simple exponential smoothing.

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Basically, this assumes that your time series fluctuates around some constant value in time.

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Therefore, what the model tries to do is it tries to learn what this average value is by using the

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WEMA in order to forecast beyond the data.

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It simply assumes that the final GWM value will propagate into the future.

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And of course, this makes sense according to the assumptions of the model, which is that the TIME

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series is a constant value, plus some random noise.

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Note that in its terminology, we call this constant value the level.

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OK, so the next model we are going to learn about is Holtze linear trend model.

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Basically, it's exactly how it sounds.

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This is a model that assumes there is a linear trend in your Time series.

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Now, how it does this is pretty cool.

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It basically uses two exponentially weighted moving averages at the same time.

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So you have one moving average for the level and you also have one moving average to learn the trend.

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The forecast is then just a linear equation using this level and trend.

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You may recall from your high school math studies that the equation for a line is Y equals M, X plus

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B or slope multiplied by X value plus intercept.

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In this case, our slope is the trend.

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Our X value is the number of steps in the forecast and our intercept is the level.

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So you can see that with this model, our forecast becomes a line that can go in any direction which

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is more powerful than the previous forecast, which had to be a horizontal line.

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The next model we will learn about is the full whole winters' model.

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This model is a model that adds seasonality.

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Basically, it's still the same concepts where we use an exponentially weighted moving average to learn

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each component.

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That is to say, in addition to the level and trend, we now have yet another moving average to estimate

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the seasonal component.

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So the seasonal component is assumed to be constant over each season.

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So what that means is if I add plus five in May, twenty twenty one, it will also add plus five and

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May twenty, twenty two plus five and May twenty, twenty three and so forth.

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So that's the basic idea.

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The seasonal component is the part of the time series that repeats every season.

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The final thing I want to mention in this lecture is that there are different ways to combine each of

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these components.

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Initially, we assume that each component was additive.

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That is the time series value is equal to the level plus the trend plus the seasonal component.

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However, it's also possible for any of these relationships to be multiplicative instead.

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So, for example, we could have the level times, the trend times, the seasonal component.

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Note that this is yet another motivation for why we take the log as a useful transformation for Time

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series.

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Recall that when you take the log of two variables being multiplied together, it turns into addition.

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In other words, the log of a product is equal to the sum of logs.

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OK, so that's the basic intuition for each technique we will study.

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Thanks for listening and I'll see you in the next lecture.