Re: How to generate synthetic econometric time series?
- To: mathgroup at smc.vnet.net
- Subject: [mg37853] Re: [mg37832] How to generate synthetic econometric time series?
- From: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>
- Date: Fri, 15 Nov 2002 01:35:23 -0500 (EST)
- Organization: Universitaet Regensburg
- Sender: owner-wri-mathgroup at wolfram.com
Dear g.
The generation of simulated data is not documented
exentsively, since it is almost trivial.
If you *have* the specification of the process, for
example
y_t = c0 + c1 y_{t-1} + c2 x_t + c3 x_{t-1} + e_t
you can generate realisations of a simulated series
recursively be replacing the e_t with random numbers
drawn from the distribution of e.
You have to set starting values for lagged variables,
for example y_{t-1}. In order to eliminate this
non-stochastic part, generate a series which is longer
than you need it and cut the leading realisations.
In Mathematica NestList or FoldList allow to
implement the procedure very elegant and efficiently.
By the way:
[1] to the best of my knowledge, the Mathematica
TimeSeries Package contains functions which generate
random series from known ARMA, VARMA,
VARIMA, and GARCH processes.
[2] MathGroup is the false address for such questions.
In MathGroup I expect questions like: I have a problem
and know how to solve it, but have problems
implementing it in Mathematica.
Your question should be asked to statisticians,
time series guys, or econometricians.
Best regards,
Johannes Ludsteck
On 14 Nov 2002 at 6:11, ginak wrote:
> Supposing that I have some historical econometric time series data
> (e.g. the price of copper from 1960 to 2001), how do I generate
> synthetic time series that have all the same statistical properties
> (including heteroskedasticity) as the historical data? Is there a
> standard recipe for doing this sort of thing?
>
> I'm not interested in forecasting; I just want to generate synthetic
> data.
>
> I've heard of ARCH/GARCH, but to my (very skimpy) knowledge these
> techniques focus on modeling volatility (a time-dependant variance?),
> which seems to me insufficient to generate synthetic data. Please
> correct me if I'm wrong.
>
> Can anyone recommend a book that discusses the mechanics of generating
> synthetic econometric data? If the book's discussion uses Mathematica
> all the better.
>
> Thanks!
>
> g.
>
>
<><><><><><><><><><><><><><><><><><>
Johannes Ludsteck
Institut fuer Volkswirtschaftslehre
Lehrstuhl Prof. Dr. Moeller
Universitaet Regensburg
Universitaetsstrasse 31
93053 Regensburg
Tel +49/0941/943-2741