Rainfall is rough

Battle Count: 56

The paper explicitly draws parallels with rough volatility theory (Gatheral et al., 2018) and Hawkes process applications in market microstructure (Bacry et al., 2013, El Euch et al., 2018). The critical heavy-tailed Hawkes process framework is directly analogous to models used for order book dynamics, endogeneity in trading, and market impact. The scaling limit to rough fractional processes mirrors the microstructure-to-volatility bridge in finance. However, the paper's primary domain is hydrology/climate, not trading.

High complexity: requires implementing linear Hawkes process simulation, spectral estimation for point processes observed via aggregated counts, second-order contrast optimization across multiple temporal scales, power-law kernel approximation by sums of exponentials, scaling limit theory for nearly critical Hawkes processes, and Hurst exponent estimation via structure functions. The mathematical machinery (Bartlett spectrum, renewal equations, Skorokhod topology) is substantial. The 8-parameter model with identifiability issues adds practical difficulty.

The paper provides detailed mathematical formulations, explicit parameter estimates in tables, and references to publicly available datasets (Météo France, Bochum via pyBL package, GHCN, paleoclimatic databases). The pyBL Python package is referenced for Bochum data. However, the full code for the spectral and contrast methods is not explicitly provided in a repository. Monte-Carlo confidence intervals are described with 100 repeated samples.