st: Lo-Mackinlay variance ratio test

[Allin Cottrell <cottrell@wfu.edu>]

For anyone interested in financial econometrics, the
SSC package lomackinlay.ado has some problems as of
version 1.0.4 (of 2006/05/23).  This module calculates 
the Lo-MacKinlay Variance Ratio test for the hypothesis 
that a variable (typically the log of an asset price) 
follows a random walk (with or without drift).  But in 
1.0.4 (don't know about earlier releases) both the 
variance ratio and the standard error of the test statistic 
are calculated incorrectly.  This applies to both the "a 
priori" standard error (assuming homoskedasticity of the
innovations) and the heteroskedasticity-robust
standard error.

For reference, I'm placing a corrected version of this 
module at

http://ricardo.ecn.wfu.edu/~cottrell/stata/lomackinlay.ado.fixed

The fixes are explained in the comments.

I show below comparative results on the log of the weekly 
NYSE close ("logp") -- data obtained from www.nyse.com. 
For small values of 'q' (the order of differencing used in
constructing the variance ratio, VR), VR is not too far
off, but the test statistic (R_s) is way off in all cases.

*** using lomackinlay.ado 1.0.4 ***

Lo-MacKinlay modified overlapping Variance Ratio statistic for logp
[  1974w3 -   1986w2 ]

q         N         VR          R_s       p>|z|
--------------------------------------------------
2        608       1.048       0.0484    0.9614
4        608       1.283       0.1511    0.8799
8        608       2.845       0.6236    0.5329
16       608       15.075      3.1977    0.0014

Lo-MacKinlay modified overlapping Variance Ratio statistic for logp
[  1974w3 -   1986w2 ]

q         N         VR          R_s       p>|z|
--------------------------------------------------
2        608       1.048       0.0421    0.9664
4        608       1.283       0.2272    0.8203
8        608       2.845       0.7453    0.4561
16       608       15.075      3.1284    0.0018

Test statistics robust to heteroskedasticity

*** using fixed version ***

Lo-MacKinlay modified overlapping Variance Ratio statistic for logp
[  1974w3 -   1986w2 ]

q         N         VR          R_s       p>|z|
--------------------------------------------------
2        608       1.039       0.9527    0.3408
4        608       1.114       1.5039    0.1326
8        608       1.185       1.5433    0.1228
16       608       1.157       0.8820    0.3778

Lo-MacKinlay modified overlapping Variance Ratio statistic for logp
[  1974w3 -   1986w2 ]

q         N         VR          R_s       p>|z|
--------------------------------------------------
2        608       1.039       0.7710    0.4407
4        608       1.114       1.2155    0.2242
8        608       1.185       1.2721    0.2033
16       608       1.157       0.7326    0.4638

Test statistics robust to heteroskedasticity

--
Allin Cottrell
Department of Economics
Wake Forest University, NC
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