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This study proposed an optimal model to examine the relationship between the Bitcoin price and six macroeconomic variables – the Bitcoin price, Standard and Poor's 500 volatility index, US treasury 10-year yield, US consumer price index, gold price and dollar index. It also examined the effectiveness of the vector error correction model (VECM) in analyzing the interrelationship among these variables. The authors employed the following approach: first, the authors sampled the period August 2010–February 2022. This is because Bitcoin achieved a market capitalization of more than US$1 tn over this period, gaining market attention and acceptance from retail, corporate and institutional investors. Second, the authors employed a VECM with the six macroeconomic variables. Finally, the authors expanded the long-run equilibrium relationship (time-invariant cointegration)-based VECM to develop a time-varying cointegration (TVC) VECM. The authors estimated the TVC VECM using the Chebyshev polynomial specification based on various information criteria. The results showed that the Bitcoin price can be modeled with the VECM (p = 1, r = 1). The TVC approach generated more explanatory power for Bitcoin pricing, indicating the effectiveness of the approach for modeling the long-run relationship between Bitcoin price and macroeconomic variables.