Gray JFE 1996 Markov Switching GARCH model

[TomDoan]

This replicates the analysis of weekly data from Gray(1996), "Modeling the conditional distribution of interest rates as a regime-switching process", J. of Financial Economics, vol 42, pp 27-62. Because the variance at time t of a GARCH process is a recursive function of all data back to the start of the data set, calculation of the true log likelihood using a Hamilton filter isn't feasible. Instead, this approximates the log likelihood by collapsing the history. In practice, Gray's model seems too broad and the method of collapsing the history too imprecise to work successfully. It's extremely difficult to get the model to fit, and it's quite easy for the branches to describe ill-behaved GARCH processes. Dueker's method (http://www.estima.com/forum/viewtopic.php?f=8&t=1190) uses a more tightly constrained collection of branches and also waits a half step longer before collapsing the historical information. The original Hamilton-Susmel switching ARCH (rather than GARCH) model (http://www.estima.com/forum/viewtopic.php?f=8&t=1193) is also a good choice in many cases---while ARCH models have largely supplanted GARCH in standard situations, with the Markov switching component added, the Markov process can provide the greater level of dependence that requires use of GARCH in a non-switching situation.

graygarch.rpf

Program file

(9.78 KiB) Downloaded 89 times

weekly.xls

Data file

(67 KiB) Downloaded 75 times