## Score-driven models

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.

## Clustering multivariate panel data

Banks are highly heterogeneous, differing widely in terms of size, complexity, organization, activities, funding choices,

and geographical reach. LSS (2018, JBES) cluster a multi-dimensional array of bank data into different bank business model groups.

Example computer code illustrating the approach is available here.

## 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.

Ox code for the CSKL observation-driven mixed-measurement dynamic factor model is here.

KLS (2012, JBES) introduce parameter-driven mixed-measurement dynamic factor models. Such MM-DFMs were subsequently

applied in e.g. SKL (2014, IJF) and SKL (2017, JAE). This Ox code refers to SKL (2017, JAE).

## Copula models with time-varying parameters

CLSZ (2018) fit a high-dimensional t-copula with time-varying volatility and correlation parameters. Connecting the dependence model

to risk exposures allows us to study risk interdependencies between different items on the consolidated Eurosystem balance sheet.

Estimation code is coming soon.

## Non-Gaussian credit risk 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).

Non-Gaussian features are furthermore occasionally appropriate to "robustify" the econometric study of heavy tailed data

from financial markets. As one approach, ES (2016, JFE) applies a factor model with t-distributed error terms instead of Gaussian ones.