  We model a portfolio of crypto assets that does not respond well to
multivariate autoregressive models because of discontinuity in conditional
covariance matrix and posterior covariance matrix caused by extreme liquidity.
We adjust asset-level return and volatility with liquidity to reduce such
discontinuity, and restore the effectiveness of a set of liquidity-adjusted
VECM-DCC/ADCC-BL models at extreme liquidity. We establish two distinctive yet
complementary portfolio liquidity measures: portfolio liquidity jump that
quantifies the effect of liquidity adjustment in forecasting the conditional
covariance matrix, and portfolio liquidity diffusion that quantifies the effect
of liquidity adjustment in estimating the posterior covariance matrix.
