Glossary

Variables

• $\mathbf{X_{t}}=(X_{1,t},\ldots,X_{d,t})$: variables of interest
• $\mathbf{S_{t}}=(S_{1,t},\ldots,S_{d_{S},t})$: factors
• $\mathbf{U_{t}}=(U_{1,t},\ldots,U_{d,t})$:
  • random variables with domain $I$
  • frequently denotes probability integral transforms of $\mathbf{X}$: $(F_{X_{1}}(X_{1}),\ldots,F_{X_{d}}(X_{d}))$
• $\mathbf{W_{t}}=(W_{1,t},\ldots,W_{d,t})$: independent random variables with domain $I$
• $\mathbf{E_{t}}$: equilibrium deviations

Copula terms

• vine: a given density decomposition
• pcc: vine and specification of used copulas
• vine perception / vine interpretation: conceived cognitive model of interpretable variables of interest

Mathematical notations

• $I$: unit interval
• $\overline{F}_{2\vert 1}$:
  • conditional cdf with domain $I$
  • frequently denotes the conditional distribution of probability integral transforms

Dimensions

• $d$: dimension of random vector $\mathbf{X} =(X_{1},\ldots, X_{d})$
• $N$: $d+d_{S}$ dimension of all variables in vine
• $T$: number of time series sample observations