Bitcoin PRESS Model

Power Law Return Sigma Signal — Bitcoin Distribution Timing

PRESS is a distributional price forecasting model, tested strictly out-of-sample over 3,135 observations across five forecast horizons. It measures where Bitcoin stands relative to its long-term power law trend and translates that into a full probability distribution of future returns. Practitioners can use this distribution for position sizing, DCA timing, risk management, or any framework that benefits from knowing the conditional return distribution. As one illustrative application, a Half-Kelly portfolio based on these forecasts outperforms buy-and-hold from 100% of possible entry dates over the 8.6-year evaluation period, with a Sharpe ratio of 0.74 vs 0.61 and maximum drawdown reduced by 10 percentage points (as of March 2026). Full technical details in Does Bitcoin's Power Law Deviation Predict Return Distributions? Evidence from the PRESS Model (SSRN).

What PRESS does

Measures structural drift: Bitcoin's price follows a long-term power law. PRESS calculates Sigma, the precise distance between the current price and this structural trend.
Forecasts distributions, not targets: Using rolling quantile regression conditioned on Sigma, the model generates a full distribution of future returns at seven probability levels rather than a single price prediction.
Actionable for portfolio construction: The full predicted distribution can be used for risk management, position sizing, or allocation decisions. The Half-Kelly portfolio shown below is one implementation; the signal itself is method-agnostic.

How to read the forecasts

Reading the percentiles: Each quantile (5%, 25%, 50%, 75%, 95%) represents a probability threshold. The 5% mark means there is a 5% chance the price falls below that level; the 95% mark means only a 5% chance it exceeds that level. Together they describe the shape of the predicted return distribution.
When sigma is negative (below trend): the distribution shifts upward, compressing downside risk and widening upside potential.
When sigma is positive (above trend): the distribution shifts downward, expanding downside risk and compressing upside.
Near zero: the conditional and unconditional distributions converge. The model correctly offers no signal.

What PRESS does not do

Not a crystal ball: It does not predict exact tops or bottoms.
Not a short-term tool: It is a structural distribution-timing tool, not a signal for day trading.
Not a shield against black swans: It cannot account for unprecedented external shocks that fall outside historical distributional patterns.

Full methodology: For technical details, out-of-sample evaluation, and robustness tests, see the research paper on SSRN.

Disclaimer: PRESS is a research model. This is not financial advice. Past performance, including historical win rates, does not guarantee future results as historical patterns may not persist.

Current 30-Day Forecast

The chart below shows the PRESS model's predicted price distribution for the next 30 days compared to the unconditional benchmark. Each point represents a quantile: the 5% mark means there is a 5% chance the price falls below that level. When the two lines diverge, the model sees a different risk profile than the historical average; when they converge, the model has no edge.

Forecast History (h = 30 days)

The shaded bands show the model's predicted price range over time. The darker the band, the higher the confidence. The orange line is the actual Bitcoin price. Hover over the price line to see the full predicted distribution at any date and whether the realized outcome 30 days later fell within the forecast range.

Price, Power Law Trend & Sigma

The orange dashed line is Bitcoin's recursive power law trend. Sigma measures how far the actual price (grey) deviates from this trend. Green shading indicates undervaluation (sigma below zero), red indicates overextension. The dashed horizontal lines (sigma = -1 and +1.5) mark extreme regime boundaries where the distributional shift is most pronounced.

Half-Kelly Portfolio Performance

These charts show the economic value of the PRESS signal. A Half-Kelly BTC/Cash portfolio uses the model's predicted distribution to size Bitcoin exposure each month. The CAGR chart compares annualised returns from every possible entry date; the excess CAGR shows the strategy's edge over buy-and-hold across time. The allocation chart reveals when the model reduced exposure before major crashes, while the drawdown comparison shows the resulting capital protection. The histogram summarises how the model allocates across time.