A moving-average (MA) component models the current time-series observation as a linear combination of current and past residual errors. It captures short-term fluctuations that autoregression and differencing do not explain, helping represent irregular variation. section 7.3.3
Use the MA component to:
- Represent dependence between an observation and residual errors from lagged observations. section 7.3.8
- Inspect ACF and PACF plots after differencing to determine whether residual autocorrelation remains. section 7.3.8
- Prefer a simpler MA specification when diagnostic plots show no significant correlations beyond lag 0. section 7.3.8
Selecting MA(0)
For a differenced time series whose ACF and PACF plots show no significant spikes beyond lag 0, choose MA(0). This indicates that no residual autocorrelation remains beyond the immediate lagged values and avoids unnecessary model complexity. section 7.3.8
