Intuitive Interpretation of priors

Classical PCA maps PC1 - 3 broadly to:

• paralell shifts
• slope
• curvature

but not precisely.

Priors should work with this and not fight it.

Market and Structural Priors

The 3 principal components map well on to macroeconomic realities:

• central bank policy
• risk premia

• convexity demand

• Statistical Regularisation priors

Intuitive Economic Priors

• smoothness priors on loadings
• sparsity / factor
• Sign constraints via half-normal priors
• Informative priors on factor variances
• Mean-reversion / dynamic priors across time

Questions

• explain how the 3 principal components map onto the 3 macroeconomic realities listed above