SteadyBlogging on Twitter (SteadyTweets?)

Tuesday, December 23, 2008

Statistics 101: ARCH/GARCH

I had planned to finally post at least a part of the Obamanomics "annotated summary" (see here), but once again got caught up doing some other stuff.

At least today it was "productive" stuff: spent a bit of time looking at models of "heteroskedasitcity", i.e., time-varying volatility:

The standard models for heteroskedasticity are ARCH & GARCH, which are imposing acronyms:
ARCH = AutoRegressive Conditional Heteroskedasticy
GARCH = Generalized AutoRegressive Conditional Heteroskedasticy

Here is the wikipedia entry, though I don't think it's particularly good (heavy on the most general equations, light on intuition):

More useful for me was reading through Jorion's brief overview in

Ch 9 of the 3rd Edition (Ch 8 in the 2nd Edition which I have) is titled "Forecasting Risks and Correlations", with a subsection on "Modeling Time-Varying Risk", which has sub-subsections on "Moving Averages", "GARCH Estimation", Long-Horizon Forecasts with GARCH", and "The RiskMetrics Approach."

The latter refers to the firm RiskMetrics; the approach the Jorion generously attributes to them is an exponential weighted moving average (EWMA) method:

Here is a paper I found by searching for "GARCH" on the RiskMetrics website:
Exploring alternative 1-month volatility forecasting techniques

I should really be more familar with this stuff that I am, given that I took a course on financial econometrics.  I need to dig out those lecture notes..and the associated Matlab code.  We didn't have a good text for the course; ostensibly it was the infamous Campbel, Lo & MacKinlay:

No comments: