Why can't we directly use an ARMA model on a series with an upward trend?

Conditions

• The model class is AR, MA, or ARMA.
• The series exhibits a non-constant mean (trend).

Reasoning, step by step

1. Identify the requirement for ARMA models: stationarity.
2. Define stationarity in this context: constant mean, constant variance, no seasonality.
3. Observe that the series has an upward trend, meaning the mean is shifting.
4. Conclude that the direct application of ARMA is invalid due to non-stationarity.
5. Introduce ARIMA as the solution, which uses differencing (the Integrated part) to remove the trend.

Example

The speaker says, "you can't just straight up use an AR or MA or even ARMA model here because those models all require the time series to be stationary." He notes the mean is shifting upward in a linear fashion.

Common misconceptions

• Thinking ARMA can handle trends automatically.
• Believing that differencing is optional for trending series in ARMA.
• Confusing stationarity with normality.

Watch the explanation

Explore next

• What does the I in ARIMA stand for and how is it implemented in the model equation?
• Why does differencing help when the original time series has a linear trend?
• What is the equation for ARIMA(1,1,1)?