Bollerslev and Mikkelson(1996) FIEGARCH Model

[TomDoan]

This is an example of estimating a FIEGARCH (Fractionally Integrated EGARCH) model from Bollerslev and Mikkelson(1996), "Modeling and pricing long memory in stock market volatility", Journal of Econometrics, vol 73, pp 151-184. The first example file does a FIGARCH, though in a bit more complicated setting than for the Baillie, Bollerslev, Mikkelson example (http://www.estima.com/forum/viewtopic.php?f=8&t=1593), since it also includes a shift variable for the variance; the second does the FIEGARCH.

Note that the FIEGARCH estimates take a very long time with a data set this size. The FIGARCH estimates, by contrast, are quite quick because the fractional integration is applied to the observable eps^2, which depends only upon the data and the mean parameters. As a result, that can be computed once at the start of each function evaluation. The DIFF instruction with FRACTION executes very quickly because it works in the frequency domain; as a result, the time requirement is on the order of T log2 T. FIEGARCH applies fractional integration to a function of eps/sqrt(h). Since the h needs to be computed recursively, there is no good alternative to crunching out the long lag filter at each data point. As a result, the time requirement is on the order of T(T+1)/2. When T is 9000, the timing ratio between FIEGARCH and FIGARCH is on the order of 100's.

figarch.rpf

FIGARCH and other GARCH estimates

(2.93 KiB) Downloaded 437 times

fiegarch.rpf

FIEGARCH and other EGARCH estimates

(3.92 KiB) Downloaded 324 times

sp500.xls

Data file

(1.72 MiB) Downloaded 456 times

[wardb]

Many thanks for the very useful FIGARCH and FIEGARCH codes provided here. Is there available an extension that provides the generalisation to the HYGARCH model described in
J. Davidson (2004) "Moment and memory properties of linear conditional heteroscedasticity models, and a new model", Journal of Business and Economic Statistics 22(1), pp16-29.

Kind regards,
BDW

[TomDoan]

In the FIGARCH code, you have the following formula for the evolution of the variance:

Code: Select all

frml varf = c+b*h{1}+uu-b*uu{1}-uufilter


For the HYGARCH model in the paper, this would be replaced with

Code: Select all

frml varf = omega*(1-beta)+beta*h{1}+alpha*uu-(beta-(1-alpha)*delta)*uu{1}-alpha*uufilter+alpha*delta*uufilter{1}


If alpha=1 and delta=0, this is the basic FIGARCH model.

[wardb]

This is "spot on". Thanks very much.