Direct and Iterated Forecasting

[CharlieEVIEWS]

Dear all,

I'm looking to compare a `direct' bi-variate single equation forecast and an 'iterated multi-step' (IMS) forecast from a bi-variate VAR, similar to papers such as http://research.stlouisfed.org/wp/2010/2010-033.pdf and the paper by Massimo, Stock and Watson quoted elsewhere on the forum. Is it possible for any of the local EViews forecast experts to tell me if the following example program is doing what I intend (for an arbitrary - h=12 horizon)?

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wfcreate m 1900 2000 genr x = nrnd genr y = nrnd !h = 12 series z=x(12) smpl 1920m1 1974m12 var var1.ls 1 2 x y smpl 1920m1 1974m12+!h equation eq1.ls z c z(-13) z(-14) y(-1) y(-2) smpl 1975m1 1975m1+!h-1 var1.fcast _fvarforecast eq1.forecast(f=na) x_feqforecast scalar rmse1 = @rmse(x_fvarforecast,x) scalar rmse2 = @rmse(x_feqforecast,x) plot x x_fvarforecast x_feqforecast

However, it is my understanding that for h=1, the direct and iterated forecasts should be equivalent, which leads me to believe that it is actually the latter program:

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wfcreate m 1900 2000 genr x = nrnd genr y = nrnd !h = 12 series z=x(12) smpl 1920m1 1974m12 var var1.ls 1 2 x y smpl 1920m1 1974m12 equation eq2.ls x c x(-1) x(-2) y(-1) y(-2) smpl 1975m1 1975m1+!h-1 var1.fcast _fvarforecast eq2.forecast(f=na) x_feqforecast scalar rmse1 = @rmse(x_fvarforecast,x) scalar rmse2 = @rmse(x_feqforecast,x) plot x x_fvarforecast x_feqforecast

which is instead correctly doing what I intend. If the latter program is not doing what I intend, exactly what is it doing?

As always, eteranlly grateful for your help.

Best wishes,

Charlie

[CharlieEVIEWS]

However, I would expect the parameters in eq2 and var1 to be different, based on the assertion that `the parameter estimates resulting from these models will vary with the forecast horizon.', which leads me to conclude that the second program is not comparing IMS and direct forecasts the way I am intending, as here, parameter estimates will be not vary with horizon. However, with the former regression (eq1), they clearly will. For the IMS VAR forecasts, the same parameter estimates are used when constructing the forecasts regardless of the horizon, which I am satisfied is being undertaken correctly.

Any thoughts greatly appreciated,

Charlie

[EViews Gareth]

Can you explain what the problem/question is for people who haven't read the papers, and don't know what a "direct bi-variate single equation forecast" or an "iterated multi-step" forecast are?

[CharlieEVIEWS]

Hi Gareth,

From the abstract of the Massimo, Stock and Watson paper:

"“Iterated” multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas “direct” forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted"

And from the first page:

"The “iterated” forecast (sometimes called a “plug-in” forecast) entails first estimating an autoregression, then iterating upon that autoregression to obtain the multiperiod forecast. In contrast, the forecast based on the multiperiod model – which, following the literature, we shall call the “direct” forecast – entails regressing a multiperiod-ahead value of the dependent variable on current and past values of the variable."

Thanks again for your help,

Charlie

[CharlieEVIEWS]

The question is: which, if either of the single equation models which the codes estimate above, are the interpretation of the `direct' forecast procedure, and whether the way that the .fcast command from the VAR add-in (as I believe it is) is undertaking an iterated forecast is as defined as I believe it is?

Charlie

[EViews Gareth]

I still don't see what the iterated one is. The direct explanation looks like a standard EViews dynamic forecast (example 2 of your code).

The var forecast does exactly the same thing as a single equation forecast.

[EViews Gareth]

Ok, having taken a quick look at the paper, I would say that the iterated procedure is what we would call a rolling forecast - I think they re-estimate the model, getting new coefficients, at each iteration of the forecast.

[CharlieEVIEWS]

Gareth, apologies if I am missing the point and being dense. Is the `iterated' forecast not different because you are 'plugging' in values for y hat, and you are not doing this in the direct single equation model as there is no equation for y? If as you stated that you thought both the var forecast (.fcast) and single equation (.forecast) forecasts were equivalent, wouldnt they give the same forecast outputs given that eq2 and var1 have the same parameter values in the sample code i whipped up above?

Thanks again,

Charlie

[EViews Gareth]

As I said above, I think the iterated forecast re-estimates the coefficients, which neither of your codes do.

The VAR forecast and the equation forecasts differ because the VAR forecast is using the dynamics of both Y and X (i.e. using forecasted values of both Y and X), whereas the equation only uses forecasts of the X, and uses actuals for Y.

[CharlieEVIEWS]

Dear All (Gareth),

A senior econometrician at my institution advised I read the Stock and Watson JBES paper on factor forecasting for a clearer exposition (http://www.benoitmojon.com/pdf/S&W-JBES ... ndices.pdf - final paragraph in section 2.1) and I feel like I have a fairly good grasp of the situation now, for which I am really truly thankful of your help (sometimes it just helps to have somebody to discuss the issues with). A h-step ahead direct forecast can be thought of as a linear projection with which to just construct the forecasts and, re-writing our example above, I believe the code is as:

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wfcreate m 1900 2000 genr x = nrnd genr y = nrnd !h = 12 'horizons smpl 1920m1 1974m12 var var1.ls 1 2 x y equation eq1.ls x c x(-!h) x(-!h-1) y(-!h) y(-!h-1) smpl 1975m1+!h 1975m1+!h var1.fcast _fvarforecast eq1.forecast(f=na) x_feqforecast scalar rmse1 = @rmse(x_fvarforecast,x) scalar rmse2 = @rmse(x_feqforecast,x) plot x x_fvarforecast x_feqforecast

and to paraphrase S&W, the iterated forecast is approach` is to develop a vector time series model for Xt, and to roll the model forward'. I interpret this as using the one-step ahead .fcast values for the variable X_t above in the same way that EViews computes its dynamic forecasts for autoregressive models (where you are not substituting in the 'true' observed values as I was in my earlier examples)....

Does this sound reasonable? As always, your comments are truly invaluable.

Best wishes,

Charlie