## Calibration of forecast means

Questions and discussions on Vector Autoregressions

### Calibration of forecast means

Hi

Is it possible to calibrate the forecast means to observed future quotes in a VAR model ?
I'm thinking that since E(y(t)) = mean, we could instead have a term structure of mean(t)
calibrated from futures on y(t) where available, such as S&P futures. Can we do that in RATS ?

thanks
Apollon
apollon

Posts: 17
Joined: Thu Sep 30, 2010 8:01 am

### Re: Calibration of forecast means

Look at the section on conditional forecasting in the User's Guide. That sounds like it's exactly what you want.
TomDoan

Posts: 2720
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Calibration of forecast means

Hi Tom

I am not looking to fix the values in advance, so I still want to keep the volatility around the mean.
Is it possible to only fix the mean ?
apollon

Posts: 17
Joined: Thu Sep 30, 2010 8:01 am

### Re: Calibration of forecast means

Conditional forecasting will give you a set of shocks which give you the mean that you want. Any mean zero noise added to those will maintain that mean. What the appropriate noise variance would be is unclear, since fixing the mean of the process is too vague a restriction to allow computing a restricted distribution for the shocks.
TomDoan

Posts: 2720
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Calibration of forecast means

Hi Tom

Assuming we are calculating base (not conditional) forecasts, can we not modify the expectations as below:

E(y(t+1)) = v(t+1) + A(1)y(t) + ... + A(p)y(t-p+1)
E(y(t+2)) = v(t+2) + A(1)y(t+1) + ... + A(p)y(t-p+2)
...

For a VAR(1) process, instead of getting the below forecast:
E(y(t+h)) = [I(k) + A(1) + ... + A(1)^(h-1)]v + A(1)^h*y(t)
we would get:
E(y(t+h)) = v(t+1) + ... + v(t+h) + ... + A(1)[y(t) + y(t+1) + ...] + ... + A(p)[y(t) + y(t+1) + ...]
The distributions are still normal with same volatilities and correlations but a time dependent mean.
In other words, we would take the results from the forecast instruction and add or subtract a constant
at a particular timestep of interest. We would do the same when calculating forecast intervals. In that case:
y(t+h) - y(t)(h) ~ N[v(t+h)-v(t), sigma(y)(h)] so that [y(t+h) - y(t)(h) - (v(t+h)-v(t))] / sigma(k)(h) ~ N(0,1)

Doesn't this make (some) sense ? Thanks.
apollon

Posts: 17
Joined: Thu Sep 30, 2010 8:01 am