The Echo Chamber

The first reflection coefficient |k1|, derived from Rabiner and Schafer's acoustic tube model of the human vocal tract (1978), is a domain-agnostic structural detector. Applied to currency and commodity markets, it measures whether a market is absorbing information or echoing it back.

A healthy market is a soundproof room. Each day's price signal is absorbed and gone. A market under structural stress is a stone canyon. Yesterday's distress signal bounces back into today's price, which bounces into tomorrow's, which bounces into the next day. The market becomes an echo chamber of its own crisis. |k1| measures how hard the walls have become.

The instrument requires no distributional assumption, no calibration, and no domain knowledge. The unit circle is the boundary by physics, not by fitting. It is derived from the Levinson-Durbin recursion — the same mathematical structure Rabiner and Schafer used to model acoustic reflection at vocal tract junctions.

The note develops the acoustic intuition, ties it to the speech-processing origin of the reflection coefficient, and validates it against 39 years of Brent crude oil prices and 28 years of China iron ore import values. A joint alert framework combining the black market premium chamber and the commodity price chamber identifies three operational states: Watch, Alert, and Demand Destruction.

Preliminary pvalidation on Sri Lanka 2021–2022 BMP and commodity price data suggests a dollar-to-domestic transmission lag of three to four months; replication requires country desk access to daily vendor price series.

Keywords: reflection coefficient, k1, Levinson-Durbin, linear prediction, black market premium, sovereign stress, reserve crisis, echo chamber, vocal tract, commodity markets