Carlos Baquero

Daniel Tinoco, Raquel Menezes, Carlos Baquero et al.

Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and variography, which can limit their effectiveness in non-stationary settings and require substantial domain expertise. In this work, we leverage an architecture based on convolutional neural networks (CNNs) for spatial interpolation that is trained and applied on a single partially observed field, without access to external data or prior fields. The model is supervised directly on the observed locations and learns to predict values at unobserved points on the user defined grid. Unlike Kriging, our method does not require explicit covariance modelling or variogram estimation, and it can flexibly capture local spatial patterns in a data-driven manner. This work demonstrates the potential of CNNs for single-instance spatial interpolation under sparse supervision, offering a practical alternative to classical geostatistical methods, and extending the use of CNNs to a new problem domain.

Carlos Baquero

Bitcoin price prediction has attracted hundreds of academic papers and continuous social media debate, yet the field lacks consensus on even basic questions: can any model beat a naive "today's price" baseline at horizons of one to six months? We survey the peer-reviewed landscape, categorize papers by evaluation methodology, and contrast academic findings with informal but substantive discourse on X/Twitter. The picture that emerges is sobering. At short-to-medium horizons, no peer-reviewed study has shown robust superiority over the naive baseline across multiple market regimes. Daily predictability is real but does not extend to hourly or monthly horizons, and may not survive transaction costs. The stock-to-flow model has failed formal out-of-sample testing, and Metcalfe's Law valuations have been challenged as spurious. The Bitcoin price power law, while empirically compelling, has not been subjected to formal distributional tests. Meanwhile, social media practitioners raise valid statistical critiques -- ordinary least squares (OLS) violations, backtest overfitting, spurious regressions -- that the academic literature has not formalized. We identify open research directions and propose concrete methodological standards for future work -- walk-forward evaluation, multi-regime holdout windows, naive baseline comparison, inclusion of zero in hyperparameter grids, and Diebold-Mariano significance testing -- arguing that the field's primary need is not more models but better evaluation.

Carlos Baquero, Raquel Menezes

Bitcoin's price has been described as following a power law (PL) in time, $P \sim t^β$ with $\hatβ\approx 5.7$ over 2010-2026. We test this claim using the Clauset-Shalizi-Newman protocol applied to Bitcoin's tail-relevant distributional series, and develop three principled time-domain adaptations of the protocol. We find that (i) the distributional power law is rejected on UTXO balances and daily |returns|, with lognormal preferred decisively; (ii) the fitted time-domain exponent varies by nearly a factor of three across reasonable shifts of the time origin -- it is not specification-robust in the sense required for a shift-invariant structural reading; (iii) standard residual diagnostics and scale-invariance tests proposed in earlier work cannot distinguish a power law from a multi-component sigmoid stack fit to the same data; (iv) Bitcoin price stands apart in a cross-asset comparison spanning Bitcoin on-chain metrics and traditional asset classes: it is the only series in the nine-series in-sample test where no single-component growth curve improves on the power law, and the quarterly $K=3$ wave-stability bootstrap rejects the PL+AR(1) null on Bitcoin at $p = 0.015$ (strict 15% CV threshold) -- a clear cross-asset separation, although not a Bonferroni-robust rejection; and (v) walk-forward Diebold-Mariano evaluation against ten candidates -- including standard time-series baselines (RW with drift, auto-ARIMA, ETS, local-linear-trend) -- shows the in-sample winner (multi-sigmoid) is among the worst long-horizon forecasters, while the simple power law dominates 12-24 month horizons against every standard baseline at $p < 0.05$, precisely because it does not commit to specific wave shapes. The fit-prediction tradeoff is the practical counterpart of the descriptive findings.

Daniel Tinoco, Raquel Menezes, Carlos Baquero

This paper presents a novel approach to classical linear regression, enabling model computation from data streams or in a distributed setting while preserving data privacy in federated environments. We extend this framework to generalized linear models (GLMs), ensuring scalability and adaptability to diverse data distributions while maintaining privacy-preserving properties. To assess the effectiveness of our approach, we conduct numerical studies on both simulated and real datasets, comparing our method with conventional maximum likelihood estimation for GLMs using iteratively reweighted least squares. Our results demonstrate the advantages of the proposed method in distributed and federated settings.