The Naive–Power Law Blend as a Robust Baseline for Bitcoin Price Forecasting

Bitcoin's price follows a well-documented power law over long time scales, yet this trend alone is a poor short-term predictor: at horizons of a few months, today's price outperforms any trend extrapolation. We construct a deliberately minimal baseline, the Naive–Power Law blend (NvPL), which interpolates smoothly from today's price (at short horizons) to the fitted power-law trend (at long horizons), and ask whether more elaborate models can beat it out of sample. We compare a broad set of alternatives: mean-reversion and momentum corrections, shrinkage regressions (ridge, LASSO, and elastic net), tree-based machine learning (gradient boosting and random forests), and 18 Bayesian structural time series specifications, some hand-specified and some discovered by an autonomous AI agent (the autoresearch pattern). Every model is evaluated on five non-overlapping two-year periods spanning distinct market conditions (2016–2026), with all tunable settings, including the baseline's own, selected on training data alone. None reliably improves on NvPL. Formal forecast-comparison tests (Diebold–Mariano, Clark–West, and the Model Confidence Set) confirm the picture: NvPL significantly beats a pure no-change forecast at one to three months, yet no correction significantly improves on it, and the confidence set retains NvPL while excluding both the naive forecast and the pure power law; the same conclusion holds under return-based and directional metrics. Aggressive in-sample tuning, including the agent's, reverses sharply out of sample, illustrating how greedy search overfits non-stationary financial data. At one to six months, short-term Bitcoin prices are dominated by persistence, and NvPL is a stringent, reproducible benchmark that more comple models should be required to beat.