Noisy Plateaus: Do Prices Remember?
Financial prices are usually represented as continuously changing processes, but at short time scales they often appear to occupy temporary local regions before moving elsewhere. This working paper calls those regions noisy plateaus and asks whether a previously established price region retains predictive relevance after the market leaves it. The framework distinguishes region formation, displacement, durable recapture, confirmed replacement, and unresolved transitions while keeping the historical region fixed after confirmation. Development tests on four previously examined Nasdaq MBP-10 files covering AAPL and INTC identified 2,667 candidate episodes, but adding historical-region features did not improve aggregate forecasts beyond geometry, recent price history, liquidity, and microstructure variables. Simple simulated processes without behavioural reference mechanisms also produced plateau-like regions and recaptures. The evidence therefore does not establish market memory, behavioural anchoring, or a trading edge. What survives is a narrower, falsifiable hypothesis: temporary price states may be a useful representation of market history, and their incremental predictive value can be tested prospectively on genuinely new data.