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Welcome back to Practical Time Series Analysis,

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and welcome to week six.

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Well, you did it.

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This is the last week of the course, almost there.

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What we'll be dealing with in this important week is the concept of seasonality.

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You can see the S in front of that SARIMA expression,

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Seasonal Auto Regressive Integrated Moving Average models.

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The idea of seasonality is pretty basic,

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pretty fundamental, and pretty obvious.

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There are lots of data sets like weather data,

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sunspot data, data having to do a tree rings,

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etc., that exhibit a regular pattern,

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a repeating pattern, a cyclic pattern,

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sales data may be like this where things are seasonal.

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So, the idea of seasonality is

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important and we bring it into our modeling in a formal model,

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the SARIMA model this week.

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We'll also deal with the concept of

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forecasting and use the technique of exponential smoothing.

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The basic idea there is that if

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you wanted to predict what the weather would be like tomorrow,

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the easiest model imaginable as far as I can see is to say,

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"well, tomorrow's going to be just like it was today."

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So we would predict one period into the future just based

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upon what was happening today in time.

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This is a pretty poor model and of course, we can do better.

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We should probably include two days ago,

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three days ago, five days ago.

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How far back though would you like to go?

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There's this idea in doing forecasting that you

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would like to privilege data points that are closer in

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time to the event you're trying to forecast

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and deemphasize those data points that are further away.

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Your old friend, the geometric series,

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will come in here,

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and will show a little bit of the mathematics

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why this brings you to exponential modeling.

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So, we deal with a single, double,

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and triple exponential smoothing and this will allow us to build models that

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do good forecasts including trend and seasonality.

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So it's very important week.

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Have a terrific week.