Endpoint-pinned price paths are not forecasts

Endpoint pinning stops at the last print

A weighted path that is required to start and end on supplied observations has no demonstrated validity beyond the last supplied observation. Endpoint pinning is that construction: the first computed value always equals the first observation, and the last computed value always equals the last observation.

Each plotted point also needs a separately computed horizontal coordinate. Editorial interpretation: those vertical and horizontal constraints keep every plotted point inside the already observed window.

Rules on the path collapse to the last point

Trading rules that appear to rest on that path are equivalent to acting on the observation used as the final computation point. Drawing the path is unnecessary for those rules and adds computation without changing the last-point equivalence.

Binomial weights make a sequence of averages

The path weights are binomial weights. They are binomial-expansion coefficients, obtainable from Pascal's triangle or from the factorial of the power divided by the factorials of the two exponents in each term.

When the two parts of the binomial sum to one, the expansion itself sums to one even as individual coefficients become large. Assigning a different observation to each term produces a weighted average of the ordered sample. Varying the two parts while keeping their sum equal to one produces a sequence of those averages.

More segments change smoothness, not the window

Increasing plotted segments from 6 to 60 changes only smoothness. The same method can also produce a path that doubles back on itself.

Seven ordered points arranged like a commodity close series, including a wider gap that could mark a missing session, were rendered as a 29-segment path.

Editorial interpretation: extra segments and a path that doubles back remain interpolation, a description of values inside the observed window. They do not create a value after that window. Linear regression is the quantitative baseline that maps ordered observations to a forecast over a stated lookback and sampling interval. An out-of-sample check then judges that baseline only on later data.