The Series - Forecasting Mechanics, Honestly

Forecasting mechanics begin with a fixed observed series. This lesson pins the data before any formula is allowed to transform it, so the arithmetic boundary is clear from the first diagram.

highlighted = computed this step

Pinned series

The series has 6 observed values. Why: every later formula is applied to this fixed integer list, so the first job is to name the evidence rather than infer a future value.

n=6

First and last values

The first value is 2 and the last value is 8. Why: the formulas consume observed values in period order, so where a value sits matters as much as the value itself.

x_{\text{first}}=2\quad x_{\text{last}}=8

Mechanics only

This book pins what each formula computes. Interpretation: the diagram is an audit trail for inputs and outputs, not a promise that the next observation will match any formula.

\text{fixed data plus fixed rule gives fixed output}

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.

\text{exact mechanics, empirical check deferred}