MAS-II: AR(1) stationarity is about a constant long-run distribution
For X_t=c+φX_(t−1)+ε_t with independent zero-mean innovations, the stationary mean is c/(1−φ) when |φ|<1. The process can fluctuate while having a constant unconditional mean and variance. Do not confuse that with a constant realised value.
Worked example or practice scenario
With c=2, φ=.6 and innovation variance 4, stationary mean is 5 and variance is 4/(1−.36)=6.25. Lag-k autocorrelation is .6^k under the model. A conditional forecast from X_t=8 differs from the long-run mean.
Try this next
Compute the one-step forecast as 2+.6×8=6.8. Then compare a multi-step forecast with 5. Check the current content outline’s time-series tasks instead of assuming an older reading list is unchanged.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.
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