The Johansen Test is a statistical procedure designed to determine the existence and number of cointegrating relationships among a set of non-stationary time series variables. Cointegration implies that two or more such series possess a long-run, stable equilibrium relationship, despite their individual short-term fluctuations. In crypto investing, its purpose is to identify pairs or groups of cryptocurrencies that exhibit stable price relationships over extended periods, providing a foundation for statistical arbitrage or pairs trading strategies.
Mechanism
The test operates on a vector autoregression (VAR) model of the time series data. It employs both eigenvalue and trace statistics to evaluate the rank of the long-run impact matrix, which directly corresponds to the number of distinct cointegrating vectors present. Essentially, it assesses whether specific linear combinations of the non-stationary series are themselves stationary, thereby signifying a stable relationship that tends to revert to a mean. The procedure incorporates adjustments for potential autocorrelation and heteroscedasticity within the data.
Methodology
The strategic methodology involves applying the Johansen Test to historical price data of related crypto assets, such as different tokens within the same blockchain ecosystem or those exhibiting clear economic linkages. Identifying cointegrated pairs enables traders to construct a spread that demonstrates stationarity, meaning it oscillates around a historical average. This allows for the implementation of mean-reversion strategies: selling the relatively overvalued asset and buying the relatively undervalued asset when the spread deviates from its equilibrium, anticipating its eventual convergence and generating profit.
Analyzing the crypto correlation term structure is a systematic process of modeling asset pair relationships across multiple time horizons to exploit mean-reversion dynamics.
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