Generalized Autoregressive Score (GAS) models, also known as Dynamic Conditional Score (DCS) models,
provide a general and entirely practical framework for the modeling of time variation in parametric models.
Time-varying parameters can be volatilities, correlations, default probabilities, loss-given-default, rating transition intensities,
the speed at which a central bank buys assets, macro or term structure factors, etc.
A brief review of the key idea is here.
Computer code is available from the www.gasmodel.com website.
Mixed-measurement dynamic factor models
Occasionally one may be interested in studying the joint variation across panel data observations for which different families of
conditional distributions are appropriate. For example, CSKL (2014, REStat) consider the joint modeling of firm rating and default
transitions (dynamic logit), macro-financial observations (normal), and loss-given-defaults (beta distribution). In bad times, defaults
and downgrades are systematically up, macros are down, and losses given default are high.
As a second example, MSK (2014) consider the joint modeling of volatile yield curves (Student-t) and central bank bond purchases
at a certain time-varying intensity (Poisson). Again, observations are dependent across sub-panels because of shared exposure to common factors.
Ox code for the CSKL observation-driven mixed-measurement dynamic factor model is here.
KLS (2012, JBES) and SKL (2014, IJF; 2016 JAE) are also based on parameter-driven mixed-measurement models.
Non-Gaussian factor models in state space form
Credit risk conditions vary substantially over time, up to an order of magnitude.
Standard portfolio credit risk and stress testing models that relate the variation in pd's to ratings and easily observed
macro-financial observations tend to fit and forecast badly, in particular in times of stress when they are needed most.
The addition of a latent factor is a practical way to study and capture the observed (excess) clustering in non-Gaussian data.
This Ox code replicates the simulation results in KLS (2011, JoE).
This Ox code refers to SKL (2016, JAE).
Non-Gaussian features are furthermore occasionally appropriate to "robustify" the econometric study of heavy tailed data
from financial markets. As one approach, ES (2015, JFE) applies a factor model with t-distributed error terms instead of Gaussian ones.