# Re: st: Time Series/ arima postestimation- How to forecast morethan one-step-ahead?

 From Robert A Yaffee To statalist@hsphsun2.harvard.edu Subject Re: st: Time Series/ arima postestimation- How to forecast morethan one-step-ahead? Date Fri, 31 Aug 2007 11:47:56 -0400

```Erika,
How you proceed depends on whether you are performing an ex ante or an out-of-sample
forecast.   Then you have to decide whether you want your forecast to be based on an
iterative projection or a structural forecast.
You have to examine the driving variable to see whether there is inherant autocorrelation
in it that needs prewhitening or another form of neutralization (using the Pankratz linear
transfer functon approach).
If you are using ex ante forecasting, you must control for that first and predict the x over
the forecast horizon. Then you can insert that data and proceed to predict the y.  Then you
need to predict the residuals to analyze them to see whether they have remaining arma errors
that need to be modeled.
If you are using an out-of-sample forecast,  Clive's approach is fine assuming that all of the
aforementioned assumptions are fulfilled.
You also have the option of resorting to the prais, newey, or the
var y , exog(x) command
Regards,
Bob Yaffee

Robert A. Yaffee, Ph.D.
Research Professor
Shirley M. Ehrenkranz
School of Social Work
New York University

Apt 19-W
2100 Linwood Ave.
Fort Lee, NJ
07024-3171
Phone: 201-242-3824
Fax: 201-242-3825
yaffee@nyu.edu
homepage: http://homepages.nyu.edu/~ray1/

----- Original Message -----
Date: Friday, August 31, 2007 5:08 am
Subject: Re: st: Time Series/ arima postestimation- How to forecast more than one-step-ahead?
To: statalist@hsphsun2.harvard.edu

> Erika Morris wrote:
>
> > I have time series data and would like to use levels of one variable
> > (X) to forecast changes in another variable (Y) over multiple periods.
> >  In other words, I want to estimate something like the following
> > equation:
> >
> > Yt+k - Yt = b*Xt + error,
> >
> > where k>1.
> >
> > It looks like the "arima" command and "predict" postestimation do
> > something similar, but based on my reading of the Time Series manual
> > they only calculate one-step-ahead forecasts. I would like to use the
> > actual value of Xt to forecast changes in Y over longer periods (k).
>
> Actually, you should be able to do this for future 'out-of-sample'
> periods using -arima-, so long as you have information on the
> regressors. This example from Kit Baum's 2004 survey lecture to the UK
>
> webuse friedman2, clear
> label var pc92 "Real Personal Consumption"
> arima pc92 L.pc92 L(0/1).m2 if tin(,1981q4)
> * static (one-step-ahead) 20-quarter forecast
> predict consump_st if tin(1982q1,1986q4)
> * dynamic (recursive) 20-quarter forecast
> predict consump_dyn if tin(1982q1,1986q4), dynamic(q(1982q1))
> tsline pc92 consump_st consump_dyn if tin(1982q1,1986q4), scheme(economist)
>  legend(cols(1) stack)
>
> The last bit is added on. The statistics in the Y variable are not
> first differences, but imagine that they are! I've used this to fit
> ARIMA models of my own, and it works very well.
>
> --
> Clive Nicholas
>
> [Please DO NOT mail me personally here, but at
> <clivenicholas@hotmail.com>. Thanks!]
>
> Baum K (2004) "SUGUK 2004 Invited Lecture: Topics In Time Series
> Modelling With Stata", available at
> http://ideas.repec.org/p/boc/usug04/7.html
> *
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```