Real life examples of AR and MA PROCESSES

Question

As someone who has just started learning ABC of timeseries can some explain me with real - life examples of what AR (autoregressive) and MA (moving-average) MODELS helps in real life.

where AR with order of p follows :

$$X_t=\mu + \alpha_1\left(X_{t-1}-\mu\right) + \alpha_2\left(X_{t-2}-\mu\right)+ \dots + \alpha_p\left(X_{t-p}-\mu\right) + e_t$$

where MA with order of q follows :

$$X_t=\mu + e_t + \beta_1e_{t-1} + \dots + \beta_qe_{t-q}$$

just a simple intuitive example that would help me like to imagine about the both processes — Devansh Gandhi, Aug 17 '20 at 08:20
The question about MA is clearly a duplicate; see ["Real-life examples of moving average processes"](https://stats.stackexchange.com/questions/45026). If you search the site, you will likely find a (near) duplicate for the AR part, too. — Richard Hardy, Aug 17 '20 at 11:37

score 0 · Answer 1 · answered Aug 17 '20 at 08:20

They are models. As somebody said: "All models are wrong, but some are useful".

For example, you can model stock prices as if they were following an AR model. Which means for example that you can try to figure out how many lags are relevant, estimate the parameters and make predictions.

Real life examples of AR and MA PROCESSES

1 Answers1