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The answer depends on what you want the time series to show, how sophisticated the audience is, how much time and effort you can put into the exercise.

A simple example to demonstrate periodicity is hourly tidal heights. Not so relevant if you live thousands of miles from the nearest sea, though.

If you want periodicity with some randomness, you can try temperatures for your locations. Either average monthly temperatures over a year (or more) or hourly temps over a day or a few days.

If you want a lot more random behaviour, go for the stock exchange prices - daily closing prices over a year, shorter term for a day.

Other economic variables: GDP, employment, unemployment rate, inflation rate can all be used but it will help to know of changes in the economic environment which resulted in the changes in the variable of your choice. For example, the unemployment rate increased because some creditor country pulled the plug on all the money your country owed it and, as a result, your country's economy went into a nose-dive.

All of these variables should be available from official sources or are either easy to collect.

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Q: What are some examples I could do for my time series class?
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