Quantitative Finance Collector is a blog on Quantitative finance analysis, methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management.

Examining the determinants of credit default swap (CDS) spreads is a hot topic, CDS spread has displayed siginificant regime switching behaviour since the break of credit crisis, which can be seen from the old graph in the post Credit Default Spread and Historical Volatility


There are sound reasons to believe that CDS spreads keep high in the period of turbulence while stay stably low during most of quiet periods. To investigate if there is possible regime switch phenomenon, I run a three year rolling panel regression using CDSs of over 250 reference entities on several widely accepted explanatory variables including: leverage, volatility, treasury yield and the spread of three month Libor and repo rates, where the last variable is used to proxy liquidity risk. The coefficients for each variable is plotted below

the coefficients of leverage and treasury yields are changing but without clear regime pattern, on the contrary, the volatility, especially the liquidity effects are suggesting there may exist regime switching and the necessity to employ a Markov regime switch model to explain CDS spreads.

PS: a matlab markov regime switching package can be found here; the panel regression is done with the R package PLM at http://cran.r-project.org/web/packages/plm/vignettes/plm.pdf

I am not a fan of Markov Regime switching model, it is hard for me to really define how high is a high regime, or how low is a low regime, let alone the method to detect the regime switch. In case you like it, here is a good package for Markov Regime Switching Models in Matlab, it provides functions for estimation, simulation and forecasting of a general Markov Regime Switching Regression.
  
Features of the package:
- Support for univariate and multivariate models.
- Support of any number of states and any number of explanatory variables.
- Estimation, by maximum likelihood, of any type of switching setup for the model. This means that you can choose which coefficients in the model, including distribution parameters, are switching states over time.
- A wrapper function for the estimation of regime switching autoregressive models, including multivariate case (MS-VAR) is included in the package.
- The values of standard error for the estimated coefficients can be calculated with 2 different methods.
- Includes a C version of hamilton’s filter that may be used for speeding up the estimation function (see pdf for details).
- Possibility of three distinct distribution assumptions for residual vector (Normal, t or GED).
- Support for reduced/constrained estimation (see pdf document for details).

This is the most up-to-date version of the switching regression procedures built by Simon van Norden and Robert Vigfusson with help from Jeff Gable. This Regime-Switching Model library lets you to estimate a general class of regime-switching models along the lines of those described in James Hamilton's textbook. Key features and limitations of the code include:
one independent variable only
two states only
arbitrary number of observed variables may be included to explain time-varying transition probablities or state-dependent means
external c-code, analytical gradients and combined maxlik()/EM algorithms for fast calculation
descriptive statistics, plots and White's model-misspecification tests
cascading estimation
separate, faster code for "simple switching" models (i.i.d. mixtures of regimes.)

learn more and download at http://www.hec.ca/pages/simon.van-norden/codepage.html and a Guide to the Bank of Canada Gauss Procedures at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=50565.

Volatility estimation and prediction is crucial for risk management, for example, the portfolio's Value at Risk (VaR) and expected shortfall are partly decided by your volatility estimated, by partly I mean other factors, like dependence structure decide their values as well. GARCH model is one of the popular models for volatility estimation, you might argue volatility regime should also be included to your model given the totally different performance (hence different parameters) between low volatility regime and high volatility regime. Here is a good paper comparing a set of different standard GARCH models with a group of Markov Regime-Switching GARCH (MRS-GARCH) in terms of their ability to forecast the US stock market volatility at horizons that range from one day to one month. To take into account the excessive persistence usually found in GARCH models that implies too smooth and too high volatility forecasts, in the MRS-GARCH models all parameters switch between a low and a high volatility regime. Both gaussian and fat-tailed conditional distributions for the residuals are assumed, and the degrees of freedom can also be state-dependent to capture possible time-varying kurtosis.

Download the paper and matlab codes at http://www.bepress.com/snde/vol9/iss4/art6/.
PS: In the codes the author multiply returns by 100 for optimization (hopefully for a faster convergence), I personally found the parameters are unstable with the change of this number. no idea if it is my data problem.