Asymmetric and Time-Varying Lag Structures in Bitcoin’s Kimchi Premium: Rolling-Window Evidence from Granger Causality and Transfer Entropy

The Kimchi Premium—the persistent price wedge between Bitcoin on Korean and global exchanges—has resisted standard no-arbitrage explanations for over seven years, raising the question of how macro-financial shocks transmit into this segmented market. Prior work relies on static, linear estimators applied over short lag horizons, leaving the timing, nonlinearity, and regime dependence of the Premium’s adjustment largely untested. We address this gap using daily data from December 2017 to December 2025 (T=2105) and rolling windows of 60, 120, and 240 trading days. Linear dynamics are tested with Granger causality (GC) and—because our return series are strongly leptokurtic (Bitcoin excess kurtosis =7.29, S&P 500 =14.77)—complemented by the Kraskov k-nearest-neighbor transfer entropy (TE) estimator, which captures conditional dependence in higher moments. Inference rests on a stationary bootstrap with pre-specified lag grids to avoid optimistic argmax bias, block-permutation tests for window-level detection rates, and Benjamini–Hochberg and Storey q-value corrections for multiple testing. Robustness is examined through conditional GC and conditional TE controlling for USD/KRW as a common factor, Toda–Yamamoto tests on price levels, a percentage-premium specification, a U.S. trading-day shift to address asynchrony, and winsorization sensitivity. We deliberately adopt a conservative inference stance at the panel level: window-level detection rates and pointwise bootstrap p-values are reported, but claims of “causality” are reserved for the within-window descriptive ranking of channels and horizons, with the panel-level null assessed by block-permutation and Benjamini–Hochberg corrections. Four empirical patterns emerge under this framing. First, Johansen tests identify a single cointegrating vector between Korean and global Bitcoin prices (trace =91.99 vs. 5% critical value 15.49), establishing the Premium as a stationary deviation from long-run parity, while none of the four macro indicators cointegrate with global Bitcoin. Second, GC detection rates for the Premium concentrate at the 240-day horizon: Gold → Premium reaches 23.3% (95% Wilson CI [19.3%,27.8%]), KOSPI 200 → Premium 16.3%, and USD/KRW → Premium 16.8%. Third, the Kraskov TE reveals an asymmetry invisible to linear tests: for Gold → Premium at w=240, the median optimal lag is five days, against one day for Gold → Bitcoin (chi-square p=0.017). Percentage-premium detection rates are substantially higher (e.g., 59.1% for Gold → Premium at w=240), indicating that the dollar-wedge specification understates causal strength. Fourth, block-permutation tests do not reject the global null of no window-level excess rejection, and Benjamini–Hochberg rejects no pair at α=0.05; we therefore read the detection-rate evidence as descriptive of localized, crisis-dependent transmission episodes rather than as panel-level rejection of pointwise non-causality, and the paper’s contribution is accordingly positioned at the level of channel ranking, lag structure, and regime decomposition rather than at the level of blanket causality claims. Crisis decomposition shows transmission is concentrated in the ETF-Halving regime (29.8% mean GC detection) and below 4% during the Terra–Luna (2.9%) and Russia–Ukraine (3.6%) episodes. The findings situate the Premium as a stationary error-correction term whose adjustment is dominated by exchange-rate and commodity channels rather than U.S. equities, with implications for arbitrage models, regulatory monitoring, and information-flow analyses of segmented crypto markets.