ARMA Model - Time Series Analysis in Python and TensorFlow
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Let’s introduce the ARMA model.
ARMA is a combination of the AR(p) and MA(q) models. Of course, ARMA stands for autoregressive moving average model.
Now, recall that we express the AR(p) model with this equation
And we can express the MA(q) model with this expression. Therefore, when we combine both models, we get the following.
Now, we have an ARMA(p,q) model with the following equations, where c is a constant, epsilon is noise, thetas are the parameters for the MA(q) model, and phis are the parameters for the AR(p) model. Just as before, q is still the order for the MA model and p is the order for the AR model.
By combining both models, we can explain the relationship of time series with both random noise, with the moving average process, and itself at a previous step, with the autoregressive portion. You must realize by now that we are starting to be able to analyze pretty complex time series.
If we plot the ACF and PACF, we notice that both plots have a decaying sinusoidal pattern. This is a clear signal that we have both an MA and AR process in play.
Let’s simulate an ARMA process in Python and see these behaviours for ourselves.
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