The simplest baseline rule repeats the last observed value. The lesson treats that as a deterministic formula output, not as evidence about what comes later.

highlighted = computed this step

Last-value rule

The naive rule repeats the last observed value, 8. Motivation: a carry-forward baseline gives a simple reference point before any smoothing choices are introduced.

naive output=xlast=8\text{naive output}=x_{\text{last}}=8
raw seriesraw seriesExact arithmetic mechanics only; no accuracy claimperiodvalue012345678214233645586

Next formula output

For period 7, the rule outputs 8. Why: no new data is used; the rule copies the last observed value exactly.

x^7=8\hat{x}_{7}=8
raw seriesraw seriesExact arithmetic mechanics only; no accuracy claimperiodvalue012345678214233645586

Baseline mechanic

Interpretation: the baseline is easy to audit because one input controls the output. That transparency is useful, but it is still not validation.

computed output is not validation\text{computed output is not validation}
raw seriesraw seriesExact arithmetic mechanics only; no accuracy claimperiodvalue012345678214233645586

Diagram note

Honesty note: These values are exact formula outputs on the pinned integer series; they do not validate what happens later. Pixel positions are rounded for layout; every number shown is exact.

the last-value rule is exact arithmetic\text{the last-value rule is exact arithmetic}
raw seriesraw seriesExact arithmetic mechanics only; no accuracy claimperiodvalue012345678214233645586