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How would you describe stationary process in plain English to someone with no mathematical background, using real life examples?

The target audience is adults with reasonable intelligence, but most have been out of school for years, if not decades.

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Strict stationarity implies that if we shift the observations in time, their distribution remains the same. This means that if we observe the stationary process last year we have a "pretty good" idea what will hapen this year. I intentionaly put "pretty good" in quotes, since due to randomness you will not be able to tell precisely what happens with stationary process in the next step, but the forecast can be pretty good. Then I would introduce AR(1) process and show how via simulations how good the forecast can be.

For real life example I would take some macroeconometric series, fit ARIMA model and then again look at the forecasts.

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