Martin Rio, Martin <[email protected]> asks how to do a dynamic prediction after
estimating a regression model with a lagged endogenous variable,
> I am using reg to estimate a time series regression of the form
>
> y(t) = a + by(t-1) + cx(t) +dz(t) + u(t),
>
> where y(t-1) was generated by lagging y one time period
>
> I want to be able to predict values of y for the later portion of my
> sample and compare these with the actual values. In models with no
> lagged independent variables I would use predict. In this model I
> want to forecast recursively, using the previous forecast to
> estimate the next, and not the predefined y(t-1) variable. If I
> use:
>
> predict yhat, bx
>
> stata uses the predefined y(t-1) variable rather than recursively
> estimating y and feeding it back into the model. What command in
> stata would do the recursive trick?
-predict- after -regress- does not truly "understand" the dynamic nature of
time-series data. But all is not lost, -predict- after -arima- does
understand time, and -arima- is happy to estimate simple regression models
without ARMA components.
If Martin's regression command were
. regress y L.y x1 x2
he could instead type,
. arima y L.y x1 x2
Let's further assume that Martin's data is monthly and he wants to begin
dynamic forecasts in April 1995. He would get the predictions by typing,
. predict y_dynhat , dyn(1995m4)
Martin can find out more in in the discussion of the dyn() and t0() options in
[R] arima.
As a side-bar, Martin may want to specify the -hessian- option on the -arima-
command to produce negative inverse Hessian estimates of the covariance matrix
(VCE), and thus the standard errors. These VCE estimates differ from the
small-sample estimates of -regress- by only a scale factor. When -hessian- is
not specified, the default covariance estimate from -arima- is the outer
produce of gradients (OPG) which differs form the Hessian estimate in finite
samples. Regardless, the parameter estimates are the same.
-- Vince
[email protected]
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