Time-varying betas for Bitcoin: A generalized cross-validation approach

We estimate a time-varying market beta for Bitcoin using a data-driven, non-parametric kernel regression framework that models how market participants weight new information relative to older information through a time-decay process. The research highlights the boundary issues inherent in the standard Akaike Information Criterion (AIC) approach for bandwidth selection of time-series kernel smoothers and applies Generalized Cross-Validation (GCV) across four distinct decay families (Exponential, Gaussian, Rectangular, and Triangular). We document the optimal kernel bandwidth that minimizes the residual sum of squares subject to the trace penalty provided by GCV. Despite the differences in optimal bandwidths for each decay family, they converge to a common effective historical lookback, confirming the rationale of the approach. Empirically, the optimized estimates reveal profound shifts in Bitcoin's market risk over time, capturing its transition from a zero-beta speculative asset pre-2020 to a highly correlated, near-unity beta asset post-pandemic.