{"id":231051,"date":"2025-09-24T11:53:12","date_gmt":"2025-09-24T15:53:12","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=231051"},"modified":"2025-09-24T11:54:40","modified_gmt":"2025-09-24T15:54:40","slug":"return-causality-among-cryptocurrencies-evidence-from-a-rolling-window-toda-yamamoto-framework","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/return-causality-among-cryptocurrencies-evidence-from-a-rolling-window-toda-yamamoto-framework\/","title":{"rendered":"Return Causality among Cryptocurrencies: Evidence from a Rolling Window Toda\u2013Yamamoto Framework"},"content":{"rendered":"\n

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#Abstract<\/strong><\/em><\/p>\n\n\n\n

We study causal linkages among six major crypto assets (BTC, ETH, BNB, ADA, XRP, LTC) using the Toda\u2013Yamamoto (T\u2013Y) framework applied in rolling windows. We emphasize the impact of multiple-testing corrections on inference.<\/p>\n\n\n\n

Raw (no-FDR) results suggest numerous causal connections, with Bitcoin often appearing as a leading driver. However, once false discovery rate (FDR) controls are applied, the network becomes much sparser: leadership is weak and intermittent rather than persistent. For example, the BTC \u2192 ETH relation is significant in only about 6.8% of windows under per-window FDR and 4.6% under global FDR, rather than being consistently strong. We document three reporting regimes\u2014no FDR, per-window FDR, and global FDR\u2014highlighting the trade-off between sensitivity and conservatism. Our results underscore the multiple-testing burden in high-dimensional causality networks (K(K\u22121) tests per window) and demonstrate that strong claims of market-wide dominance do not survive conservative adjustment.<\/p>\n\n\n\n

Introduction<\/a><\/h1>\n\n\n\n

Cryptocurrencies are frequently portrayed as highly interconnected, with Bitcoin often assumed to be the primary driver of market dynamics. While Bitcoin\u2019s size and visibility make this assumption plausible, formal statistical testing is required to assess whether causal leadership is strong and persistent.<\/p>\n\n\n\n

This study investigates causal linkages among six widely traded assets \u2014 Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), Cardano (ADA), Ripple (XRP), and Litecoin (LTC). Using the Toda\u2013Yamamoto (T\u2013Y)<\/p>\n\n\n\n

causality framework, we test directional predictability both in the full sample and within rolling windows. Our analysis emphasizes the importance of controlling for multiple testing. In a setting with K assets, there are K(K\u22121) pairwise directional tests per window (30 tests when K=6), which strongly inflates raw significance rates. We therefore contrast three reporting regimes:<\/p>\n\n\n\n

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  1. No correction (raw p-values),<\/li>\n\n\n\n
  2. Per-window FDR (controlling discoveries within each window), and<\/li>\n\n\n\n
  3. Global FDR (controlling across all windows and pairs, most conservative).<\/li>\n<\/ol>\n\n\n\n

    The results show that raw tests yield many apparent causal connections and suggest Bitcoin as a frequent leader. However, after FDR adjustment, most links disappear, and Bitcoin\u2019s role becomes weaker and intermittent. A handful of other relations \u2014 such as ADA \u2192 XRP and XRP \u2192 ETH \u2014 appear more persistent under the less conservative per-window FDR. Only a small number of edges survive global-FDR adjustment.<\/p>\n\n\n\n

    Crypto Causality Analysis (Toda\u2013Yamamoto + Rolling Stability)<\/a><\/h1>\n\n\n\n

    This notebook contains a full, runnable pipeline to:<\/p>\n\n\n\n