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What is an ARIMA model?

As usual, we’ll start with the notation. An ARIMA model has three orders – p, d, and q (ARIMA(p,d,q)). The “p” and “q” represent the autoregressive (AR) and moving average (MA) lags just like with the ARMA models. The “d” order is the integration order. It represents the number of times we need to integrate the time series to ensure stationarity, but more on that in just a bit.

Convention dictates that we always enter the three orders in the same way – “p” first, then “d” and finally – “q” (ARIMA(p,d,q)). Of course, that’s because “p” represents the AR components, “d” the Integrated ones and “q” the MA ones.

How is ARIMA related to ARMA?

Any model of the sort ARIMA (p, 0, q) is equivalent to an ARMA (p, q) model since we are not including any degree of changes. Of course, an ARIMA (0, 0, q) and an ARIMA (p, 0, 0) would also be the same as an MA(q) and an AR(p) respectively.

Now that we’re familiar with the notation and how the different types of models are connected, we can continue with the intuition.

How do ARIMA models work?

These integrated models account for the non-seasonal difference between periods to establish stationarity.

Hence, even the AR components in the model should be price differences, (ΔP) rather than prices (P). In a sense, we are “integrating” “d”-many times to construct a new time-series and then fitting said series into an ARMA (p, q)

What is an ARIMA model?

As usual, we’ll start with the notation. An ARIMA model has three orders – p, d, and q (ARIMA(p,d,q)). The “p” and “q” represent the autoregressive (AR) and moving average (MA) lags just like with the ARMA models. The “d” order is the integration order. It represents the number of times we need to integrate the time series to ensure stationarity, but more on that in just a bit.

Convention dictates that we always enter the three orders in the same way – “p” first, then “d” and finally – “q” (ARIMA(p,d,q)). Of course, that’s because “p” represents the AR components, “d” the Integrated ones and “q” the MA ones.

How is ARIMA related to ARMA?

Any model of the sort ARIMA (p, 0, q) is equivalent to an ARMA (p, q) model since we are not including any degree of changes. Of course, an ARIMA (0, 0, q) and an ARIMA (p, 0, 0) would also be the same as an MA(q) and an AR(p) respectively.

Now that we’re familiar with the notation and how the different types of models are connected, we can continue with the intuition.

How do ARIMA models work?

These integrated models account for the non-seasonal difference between periods to establish stationarity.

Hence, even the AR components in the model should be price differences, (ΔP) rather than prices (P). In a sense, we are “integrating” “d”-many times to construct a new time-series and then fitting said series into an ARMA (p, q)

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