**hl <rho1> <rho2> <incr> <y> = <x1>, [<x2> [, <x3> [, ... [, <xn>]]]]**In the Hildreth-Lu procedure, a guess of the autocorrelation coefficient of the errors,

*rho*, is chosen, multiplied by the equation lagged once, and subtracted from the unlagged equation. The resulting equation then is estimated by ordinary regression. Another value of the guess of*rho*then is chosen and the process repeated. In this command, <rho1> is the starting guess of*rho*, <incr> is the amount by which it is incremented on each iteration, and <rho2> is an upper limit on the guess. The <y> and <x1>, ..., <xn> values are as in the*r*command.At the end of the process, you will get a table with this heading:

RHO-HL SEE 1 AHEAD RHO-EST SEE LONG-RUN

RHO-HL shows the assumed

*rho*, the SEE 1 AHEAD shows the standard error of estimate (SEE) of the estimated equation, RHO-EST shows the*rho*of the estimated equation, and SEE LONG-RUN shows the standard error using the fitted equation on the original, undifferenced data, without a knowledge of the true lagged value of the dependent variable, as must be done in forecasts of more than a few periods ahead. If the*save*command is on, all of the estimated equations will placed in the .SAV file as undifferenced equations suitable for going into a model. You must choose which one you want.For graphing the HL output, one should run the equation one last time with the chosen value of

*rho*as both the starting and ending*rho*. Then also run the equation with just the*r*command (no autocorrelation). Finally, construct two graphs:gr depvar predp1 hlshort gr depvar predic hllong

The first will compare the actual with two one-period ahead forecasts, the one from ordinary least squares (+’s) and one from Hildreth-Lu (x’s). The second compares the actual with two forecasts not relying on the lagged value of the dependent variable. Again, the uncorrected least squares fit is shown by +’s and the fit using the H-L correction is shown by x’s.

The pauses at the end of each fit in the HL procedure can be eliminated by the

*zip*command. If you use*zip*, however, you must remember to do “zip off” before using the*(gr)aph*command.*G7*does not provide the Corchrane-Orcutt correction, since Hildreth-Lu is better.