Applying time delay convergent cross mapping to Bitcoin time series

Abstract

This paper explores the applicability of Convergent Cross Mapping (CCM) and its extension, Time Delay Convergent Cross Mapping (TDCCM), to assess the causal relationships between Bitcoin, the S&P 500 index, and gold. Unlike conventional causality analysis methods, such as Granger causality or transfer entropy, CCM accounts for non-separable, weakly connected dynamic systems, and TDCCM explicitly incorporates time lags during cross-mapping, enabling the detection of complex causal relationships in systems with shared nonlinear behavior. This makes it particularly suitable for financial time series that often exhibit chaotic and nonlinear dynamics, particularly during periods of market instability. We integrate TDCCM with simplex projection and sequential locally weighted global linear map (S-map) algorithms, applying a sliding window approach to identify short time intervals characterized by high levels of nonlinearity and chaoticity. Using this approach, we uncovered a strong causal relationship between Bitcoin and the S&P 500 index during the onset of the COVID-19 pandemic. Our analysis reveals a bidirectional causal relationship between Bitcoin and the S&P 500 index, highlighting their interconnectedness during periods of heightened economic uncertainty. Furthermore, we find a unidirectional causal influence of Bitcoin on gold, reflecting Bitcoin’s evolving role as a macroeconomic indicator and its growing relevance as an alternative store of value. These findings provide insight into the dynamics between cryptocurrencies and traditional financial markets, particularly during periods of global economic disruption.