The Window Tradeoff - Forecasting Mechanics, Honestly

Changing the window changes the arithmetic sequence. A shorter window uses fewer inputs, while a longer window spreads each output over more observed values.

highlighted = computed this step

Shorter window

MA(2) starts at period 2 and outputs 3 there. Motivation: a shorter window can react earlier because it waits for fewer observed values.

MA_{2}\text{ first output}=3

MA two sequence

The MA(2) outputs are 3, 7/2, 9/2, 11/2, and 13/2. Why: each is the exact average of two adjacent values, so the shorter row is still fully auditable.

\text{MA}_{2}=3,7/2,9/2,11/2,13/2

Window tradeoff

The table compares MA(2) and MA(3) over the same displayed periods. Interpretation: a larger window smooths the arithmetic over more inputs and can move more slowly, but the table alone does not rank accuracy.

\text{compare overlapping periods}

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{window length changes the arithmetic sequence}