## Hodrick(1992) Standard Errors

Questions and discussions on Time Series Analysis

### Hodrick(1992) Standard Errors

This is an example of the calculation of Hodrick(1992) standard errors: "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement", Review of Financial Studies, vol 5, no 3, 357-386. The data file is attached. This is a calculation which is specific to multiple step predictability regressions as it uses the one-step residuals to compute the covariance matrix for multiple step regressions, and computes them under the null of no predictability. In other words, it's not a general purpose method for computing standard errors, but is an alternative method for calculating predictability test statistics.

There is now a separate procedure which does this calculation. See

http://www.estima.com/forum/viewtopic.php?f=7&t=993

Code: Select all
`** Example of calculation of Hodrick(1992) standard errors.* "Dividend Yields and Expected Stock Returns: Alternative Procedures* for Inference and Measurement", Review of Financial Studies, vol 5, no* 3, 357-386.** 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.*calendar(m) 1988:11open data aluminum.xlsdata(format=xls,org=columns) 1988:11 2007:05 pzalul pzalul3*set logspot = log(pzalul)set logforw = log(pzalul3)set ret3    = logspot{-3}-logspotset ret1    = logspot{-1}-logspotset xchange = logforw-logspot** To compute Hodrick(1992) standard errors, first compute a one-period* predictability regression. Residuals here should be serially* uncorrelated.*linreg ret1 / eps# constant xchange*linreg ret3# constant xchange*compute k=3dec symm s0dec vect wkcompute s0=%zeros(%nreg,%nreg)do time=%regstart()+k,%regend()   compute wk=%zeros(%nreg,1)   do i=0,k-1      compute wk=wk+eps(time)*%eqnxvector(0,time-i)   end do i   compute s0=s0+%outerxx(wk)end do time** Same regression with Hodrick standard errors*linreg(lastreg,create,covmat=%xx*s0*%xx,form=chisq,\$ title="Least Squares with Hodrick standard errors")** And with Newey-West standard errors*linreg(lastreg,lwindow=newey,lags=k-1,\$ title="Least Squares with Newey-West standard errors")`

aluminum.xls
TomDoan

Posts: 2727
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Hodrick(1992) Standard Errors

Mr TomDoan, I would like to use the calculation that you proposed for Hodrick (1992) standard errors. My preocupation is that i have already calculated the agregations for my series on excel. So I would like to know if i have to use only the basic series (not aggregated) and your programma will calculate them for me, or do i have to use the series already aggregated. In this case, what is the meaning of the parameter "k" ?
I am waiting for a quick reply
Thanks

Dario Lebelon
Student
Dario

Posts: 3
Joined: Wed Mar 16, 2011 2:19 pm

### Re: Hodrick(1992) Standard Errors

I'm confused about what you've already calculated in Excel. You must have the original spot and forward data, so the simplest thing to do would be to read that into RATS and adapt the program given. If you've done some of the matrix calculations in Excel, I really couldn't tell you what you could do with them.
TomDoan

Posts: 2727
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Hodrick(1992) Standard Errors

Ok. I am making a regression of excesses return (rt) on realised volatility (rv). And i want to make k-step regression to see for wich value of k the rv predict rt. In the litterature, it seem that rv is good predictable variable for rt but only il the long run. So on excel i begin to sum my data over k periods (that's what i call aggregate data). for value of k= 1, 3 , 6, 12, 24.... until 120 months
I add an excel file that show you briefly how i calculated the agregation for k = 3 and then k =6 (only) where k is the horizon of my regression. The point is that when i used your program to calclulated the Hodrick (1992) standard errors, according to you wich value of k do i have to use? I see on your example you used k=3 (Compute k=3)...So do i have to run all my aggregated data with k=3???
I didn't make any matrices on excel...

Dario L.
Student
Attachments
k step regression.xls
K step aggregation
Dario

Posts: 3
Joined: Wed Mar 16, 2011 2:19 pm

### Re: Hodrick(1992) Standard Errors

Dario wrote:Ok. I am making a regression of excesses return (rt) on realised volatility (rv). And i want to make k-step regression to see for wich value of k the rv predict rt. In the litterature, it seem that rv is good predictable variable for rt but only il the long run. So on excel i begin to sum my data over k periods (that's what i call aggregate data). for value of k= 1, 3 , 6, 12, 24.... until 120 months
I add an excel file that show you briefly how i calculated the agregation for k = 3 and then k =6 (only) where k is the horizon of my regression. The point is that when i used your program to calclulated the Hodrick (1992) standard errors, according to you wich value of k do i have to use? I see on your example you used k=3 (Compute k=3)...So do i have to run all my aggregated data with k=3???
I didn't make any matrices on excel...

Dario L.
Student

You would use a different value of k for each length of aggregation. I wrote a procedure which does the calculation above and takes the number of steps as an input which should make it easier to use.

http://www.estima.com/forum/viewtopic.php?f=7&t=993
TomDoan

Posts: 2727
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Hodrick(1992) Standard Errors

Thank you!
Dario

Posts: 3
Joined: Wed Mar 16, 2011 2:19 pm