Power laws, AI models often memorize Bitcoin market noise

A May 2026 preprint by Carlos Baquero of the University of Porto reviews peer‑reviewed research on Bitcoin price forecasting and reports frequent failures to beat simple naive benchmarks at one‑ to six‑month horizons. The review examined 23 influential studies selected for methods, impact or use of out‑of‑sample tests.

The preprint states, “no model had demonstrated durable superiority over the appropriate naive benchmark at horizons of one to six months across several market regimes.” The review identified recurring weaknesses in model evaluation and out‑of‑sample testing.

One factor the review highlights is persistence in prices. Forecasts that project today’s price forward can produce small percentage errors over short horizons because prices often move slowly relative to their level. That makes a benchmark based on current price hard to beat on one‑day or one‑week horizons.

The review identifies non‑stationarity as a limiting factor for longer horizons. Bitcoin’s liquidity, user base, derivatives structure and investor access changed over the past decade. Models calibrated to data from the 2017 retail cycle encountered a different derivatives market in 2021, and the launch of spot ETFs in 2024 altered flows and price discovery. A relationship that held in one period can disappear as market conditions change.

Independent studies cited in the review reached similar results. A study by Francesco Puoti, Fabrizio Pittorino and Manuel Roveri tested 12 forecasting methods on five major cryptocurrencies at one‑day, seven‑day and 30‑day horizons and found naive models consistently outperformed ARIMA, Prophet, random forests, XGBoost, LSTM networks and N‑BEATS. That study concluded the outcome reflects limits on the available information rather than the sophistication of the methods.

The review also cites research on backtest overfitting. David Bailey and colleagues formalized how trying many model variants raises the chance of finding an apparently excellent historical result by luck. Baquero reports many papers present a single successful backtest without disclosing how many alternatives were tried. The review notes that walk‑forward validation and multiple non‑overlapping holdout windows provide stronger evidence, but none of the examined papers tested the same approach across several non‑overlapping regimes.

Information leakage is listed as another common flaw. Features computed with future data, normalization across the full sample and overlapping return windows can leak future information into training. Complex model architectures can hide those leaks. The review says evaluation metrics can mislead when a low level‑error masks incorrect trading signals, and that most studies omit trading costs.

Valuation narratives are addressed in the review. Frameworks such as stock‑to‑flow, Metcalfe‑style network value and power‑law scaling often fit historical data in sample but show limited predictive power out of sample. The review cites a 2024 peer‑reviewed study by Alexander Shelton that found stock‑to‑flow and Metcalfe variables explained returns in sample but lost predictive strength once time effects were introduced. A study by Savva Shanaev and co‑authors used instrumental variables and found that once autocorrelation and the two‑way link between activity and price were accounted for, apparent effects of hashrate and transaction counts on value disappeared.

On power laws, the review notes that a high R‑squared on a log‑log chart confirms a line fits the observed sample but that formal support requires testing residual distributions, sensitivity to the start date and out‑of‑sample performance. Baquero reports the power‑law literature has not completed those tests.

The preprint recommends publishing the naive benchmark alongside new models, reporting results by market regime, including trading costs, releasing code and data for replication, and disclosing how many model variations were tested. It also recommends separating valuation narratives from point forecasts and allowing a corrective term that can be zero so a model may conclude that today’s price is its best prediction when no additional signal exists.