What does the d in ARIMA(p,d,q) mean?

Conditions

• The model is denoted as ARIMA(p,d,q).
• $d$ is a non-negative integer.

Reasoning, step by step

1. Identify the three parameters p, d, and q in the ARIMA notation.
2. Recognize that p is the autoregressive order and q is the moving-average order.
3. Define d as the integrated order or differencing order.
4. Explain that $d=1$ means first differencing ($Z_t = q_{t+1} - q_t$).
5. Explain that $d=2$ means second differencing ($W_t = Z_{t+1} - Z_t$).

Example

The speaker states, "d is the order of the integrated part and that here $d=1$ because they took the first difference." The board shows ARIMA(1,1,1) with p,d,q written beneath it.

Common misconceptions

• Confusing d with the number of data points.
• Thinking d refers to the degree of a polynomial trend.
• Believing d can be negative.

Watch the explanation

Explore next

• When would you use a second difference instead of a first difference?
• What is the equation for ARIMA(1,1,1)?
• How is the differenced series $z_t$ defined from the original series $q_t$?