GARCH vs EWMA

[afterworkguinness]

Hi David,
In the practice questions on Hull chapter 12 there is a question that asks "What does Hull cite as an “attractive feature of EWMA?" citing the below quote from Hull as the answer. Isn't the same answer true for GARCH(1,1) (ok I know it has the omega term, but how much computational difficulty is added by that ?)

The EWMA approach has the attractive feature that relatively little data
need to be stored. At any given time, only the current estimate of the variance rate and the
most recent observation on the value of the market variable need be remembered. When a
new observation on the market variable is obtained, a new daily percentage change is
calculated and equation (21.7) is used to update the estimate of the variance rate. The old
estimate of the variance rate and the old value of the market variable can then be
discarded.

 

[ShaktiRathore]

Hi,
According to me the stated advantage is relative to MA method where a large amount of data needs to be stored. In Garch you have same data requirement as EWMA except that there is an additional long run variance term which is needed to be stored. This long run average variance is constant for a period and it needs to be calculated for a period for which we require data which increases the computational difficulties and data requirements. In addition you require to estimate the omega term from this long run variance. Hence certainly Garch model do add to data and computational requirements as compared to EWMA. So overall EWMA is the most attractive when it comes to data storage.
thanks

 

[David Harper CFA FRM]

Hi afterwork,

In a literal sense, I agree: if the GARCH params are stable, then a GARCH volatility update is just like a EWMA volatility update. As the unconditional variance term (omaga = LR variance * weight) is a constant, the other terms (lag variance and lag innovation) are essentially the same recursive reductions as EWMA (i.e., both are exponential weight updates). Without the omega term, GARCH and EWMA are mathematically identical.

Okay, but the inclusion of the omega term, and the underlying theory, is a big difference in practice: the GARCH params are typically estimated with a statistical producure (eg, MLE) which wants a dataset (contrast with "relatively little data need to be stored") whereas, according to Carol Alexander at least, "on the choice of [EWMA] lambda, yet there is no statistical procedure to explain how to choose it" ... "more often lambda is chosen subjectively." This matters also because the unconditional (long-run) variance is the key input into the GARCH forecast; contrast with EWMA's arguable inability to forecast. In summary, the omega term is supported by a higher theory set and wants data (to fit params) and its resultant sophistication makes it less simple. In this way, the omega term is deceiving: it suggests the want of data, whereas lambda in EWMA is far less statistically demanding. I hope that helps,

 

[afterworkguinness]

I didn't think of that. Thanks David and Shakti.

 

[David Harper CFA FRM]

sure, it got me thinking. I'd go so far as to argue that EWMA's lambda is a bit "fire and forget" (i.e., pick lambda, let it be). Versus GARCH, which almost insists that it parameters get updated regularly (so "hangs on" to the trailing data). Thanks,