Python Tutorial: Intro to AR, MA and ARMA models

Want to learn more? Take the full course at https://campus.datacamp.com/courses/arima-models-in-python at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- Now you know how to prepare your data, lets dive straight into the models. We will discuss AR and MA models and how these are combined into ARMA models. In an autoregressive model we regress the values of the time series against previous values of this same time series. The equation for a simple AR model is shown here. The value of the time series at time t, is a-one times the value of the time series at the previous step. There's also a shock term, epsilon-t. The shock term is white noise, meaning each shock is random and not related to the other shocks in the series. a-one is the autoregressive coefficient at lag one. Compare this to a simple linear regression where the dependent variable is y-t and the independent variable is y-t-minus-one. The coefficient a-one is just the slope of the line and the shocks are the residuals to the line. This is a first order AR model. The order of the model is the number of time lags used. An order two AR model has two autoregressive coefficients, and has two independent variables, the series at lag one and the series at lag two. More generally, we use p to mean the order of the AR model. This means we have p autoregressive coefficients and use p lags. In a moving average model we regress the values of the time series against the previous shock values of this same time series. The equation for a simple MA model is shown here. The value of the time series, is m-one times the value of the shock at the previous step; plus a shock term for the current time step. This is a first order MA model. Again, the order of the model means how many time lags we use. An MA two model would include shocks from one and two steps ago. More generally, we use q to mean the order of the MA model. An ARMA model is a combination of