Autoregressive moving average model

Have you ever played with a yo-yo, where the yo-yo goes up and down over and over again? That's kind of like what an autoregressive moving average (ARMA) model does, but with numbers instead of a toy.

The "autoregressive" part of the model means that it looks at the past values of a certain variable (like temperature, stock price, or whatever you want to study) to predict what the next values will be. It's like looking at the yo-yo's past movements to predict where it will go next.

The "moving average" part of the model means that it also takes an average of the past values, and then adds or subtracts that average number from the predicted value. This is like trying to smooth out the movement of the yo-yo, so that it's not so jerky and it's easier to see where it's going.

So an ARMA model combines both of these techniques to predict what will happen next with a certain variable (like temperature, stock price, or whatever). It looks at the past values of that variable, and takes an average of those past values to help make a more accurate prediction. Just like how if you watch the yo-yo carefully and try to predict where it will go based on what it's done before, you can get pretty good at it over time!