OLSHODRICK Procedure

@OLSHODRICK computes a least squares regression with the covariance matrix proposed by Hodrick(1992). Note that the calculation is specific to multiple step predictability regressions. It uses the residuals from a one-step regression to compute the covariance matrix for a k-step regression. With STEPS=1 (that is, evaluating just the one-step ahead prediction), it's equivalent to Eicker-White standard errors (what you would get with LINREG with the ROBUSTERRORS option). With multiple step predictions, the errors would be expected to be serially correlated (up to order STEPS-1), but with a particular structure, which is exploited by Hodrick's procedure, and won't be used by other HAC standard error calculations (such as Newey-West).

@OLSHodrick( options ) depvar start end

# list of explanatory variables

Parameters

depvar	dependent variable
start, end	range to estimate, defaults to maximum range permitted by all variables involved in the regression.

Options

STEPS=number of steps for the predictability regression

ONESTEP=one-step-ahead analogue to thedepvar

EPS=one-step-ahead residuals

You must supply the STEPS option and either ONESTEP or EPS.

[PRINT]/NOPRINT

Example

calendar(m) 1988:11

open data aluminum.xls

data(format=xls,org=columns) 1988:11 2007:05 pzalul pzalul3

set logspot = log(pzalul)

set logforw = log(pzalul3)

set ret3 = logspot{-3}-logspot

set ret1 = logspot{-1}-logspot

set xchange = logforw-logspot

* Linear regression of three step ahead returns with conventional standard errors

linreg ret3

# constant xchange

* Same with Hodrick standard errors. ONESTEP=RET1 provides the one step ahead returns

* for computing the one-step residuals.

@OLSHodrick(steps=3,onestep=ret1) ret3

# constant xchange

* And with Newey-West standard errors

linreg(lwindow=newey,lags=2) ret3

# constant xchange