Shrinkage estimator versus time series with decay.

[allépourpêcher]

Example of time series with decay:
JP Morgan rule for predicting vol. Vol^2 =last period vol^ plus random noise^2.
What’s the difference between these two ideas?
I’ve searched the forum but nothing doing……
Thanks,
APP

 

[elcfa]

Not sure what you mean by JP Morgan rule, but the two estimators from CFAI differ in the following way (quote from memory, so may be slightly wrong).
1. Shrinkage estimators: adjust/moderate forecast using historical data with data from another model/forecast (e.g., multi-factor model).
2. Time series estimators: adjust forecast using historical data by adding more weight to near-term volatility because of volatility clustering, particular with high frequencies (daily, weekly) at some markets.
Is this what you mean?

 

[allépourpêcher]

Hi,
Thanks for the reply. I think you’ve helped me to understand this. I’ve done some re-reading also.
Shrinkage estimators seem to one part value derived from a range of historical data (e.g. mean/covariance) and one part #Some other Estimate# from a model.
Time series estimators are modelled from one or more single historic values as per LII. In the case of the time series with decay, the recipe is one part actual historic values and another part decay constant*random error. As you say, volatility clustering is a rationale for this approach.
I guess I was getting hung up on the idea that they we both modifying past data, and couldn’t differentiate between the two ideas.
Thanks,
APP
PS. I miswrote that JP morgan rule for volatility (corrected below) which is referenced as a time series estimator.
JP Morgan rule for predicting vol. Vol^2 =last period vol^2 plus random noise^2.

 

[happyking02]

How about the multifactor model that follows in the CFAI? can anyone please explain the difference of formula 3a and 3b, (CFAI Vol 3, Page 31)

 

[elcfa]

happyking02 Wrote:
——————————————————-
> How about the multifactor model that follows in
> the CFAI? can anyone please explain the difference
> of formula 3a and 3b, (CFAI Vol 3, Page 31)
3a is for variance (variance with itself)
and 3b for covariance (variance with another variable)
The basic model: return is driven by a couple of drivers (factors).
In a sense, the CAPM is a specific case of the multi-factor case since you have only ONE variable: the market itself.
It should be noted that CAPM requires that market is in equilibrium, while multi factor model does not.

 

[onlysimon]

allépourpêcher wrote:. Vol^2 =last period vol^ plus random noise^2.

not completelyclear on this.
the VIX is a measure of “implied volatility” not actual volatility. so any change in the VIX obviously subject to all the biases which has been discussed.
Are they talking about actual past vol, vs. implied future vol? no reason why they need to work together lock step. and you would expect to see put/call differences do to investor leverage changes etc etc.
(AND there is a subtle difference between geometric decay and exponential decay)