sas >> Statistical test for difference between two numbers

by abhaykaushik » Thu, 29 Nov 2007 22:15:00 GMT

Hi,
I have two series of hedge funds with monthly observations. First series
has 51,300 monthly observations and second has 12,340 monthly
observations. I ran an OLS for both:

model Rs = RMRF SMB HML UMD; and I get average monthly coefficients of
intercept and betas.
Alpha of first series is -0.00288 and for the other one is 0.00054. Now I
want to test whether the difference between these two (-0.00288 -0.00054)
is statistically different? More specifically the annualized alpha
difference, i.e. (aplha1*12-alpha2*12)
Is there any test that can be performed to check this statistical
difference?

Thanks


sas >> Statistical test for difference between two numbers

by sonik son » Fri, 30 Nov 2007 02:03:45 GMT





You may want to look at PROC ANOM (analysis of means.) It allows you
to compare two means to determine if they are statistically different.
There are also some helpful graphical outputs to graphically simplify
this concept for management, should they be less statistically
oriented (i.e. "dullards".)



sas >> Statistical test for difference between two numbers

by peterflomconsulting » Fri, 30 Nov 2007 02:14:56 GMT

>> Hi,
I have two series of hedge funds with monthly observations. First
series has 51,300 monthly observations and second has 12,340 monthly
observations. I ran an OLS for both: model Rs = RMRF SMB HML UMD;
and I get average monthly coefficients of intercept and betas.

Alpha of first series is -0.00288 and for the other one is 0.00054.
Now I want to test whether the difference between these two (-0.00288
-0.00054) is statistically different? More specifically the annualized
alpha difference, i.e. (aplha1*12-alpha2*12)

I suggest a permutation test.

There's a paper by David Cassell called Don't be Loopy that may be of help
Basic idea:
Combine all the intercepts into one variable
Randomly pull out sets of 51,200 and 12,340 intercepts
Do this many times
See how many times the difference is as big as the one you got

But with such huge data sets, even a small difference is likely to be statistically significant, so I suggest first thinking whether this is really what is important to you.

HTH

Peter


Statistical test for difference between two numbers

by HERMANS1 » Fri, 30 Nov 2007 03:47:53 GMT

I wouldn't worry too much about the statistical significance of the
difference between estimates of a model that almost certainly have both
substantial bias and underestimated confidence bounds. OLS estimates of
time series do not take into account seasonal variation, trends, or
cycles in time series. Because assumptions about the independence of
error terms almost never hold, time series require special estimation
and forecasting methods. For that reason SAS has a separate product that
includes statistical procedures tailored to time series analysis
(SAS/ETS). If you are looking for differences in trend between two time
series, review the documentation of SAS/ETS first. A clever adaptation
of PROC MIXED or a non-linear equivalent might work as well as some of
the SAS/ETS PROC's, but would take much more time and expertise to
specify.

An OLS estimate of a trend in a time series fits the sample used to
estimate it much better than it fits another sample or a future
projection of the same sample. The difference in two biased and
inefficient estimates won't tell you much. As recent discrepancies
between predictions of credit and other financial models and observed
values show, estimates of parameters of time series models tend to be
inaccurate at best. Using inappropriate estimation methods adds
confusion to weak information. Sorry to be so negative, but don't go
there.
S

-----Original Message-----
From: XXXX@XXXXX.COM [mailto: XXXX@XXXXX.COM ]
On Behalf Of Abhay Kaushik
Sent: Thursday, November 29, 2007 9:15 AM
To: XXXX@XXXXX.COM
Cc: Abhay Kaushik
Subject: Statistical test for difference between two numbers


Hi,
I have two series of hedge funds with monthly observations. First
series has 51,300 monthly observations and second has 12,340 monthly
observations. I ran an OLS for both:

model Rs = RMRF SMB HML UMD; and I get average monthly coefficients of
intercept and betas. Alpha of first series is -0.00288 and for the other
one is 0.00054. Now I want to test whether the difference between these
two (-0.00288 -0.00054) is statistically different? More specifically
the annualized alpha difference, i.e. (aplha1*12-alpha2*12) Is there any
test that can be performed to check this statistical difference?

Thanks


Statistical test for difference between two numbers

by abhaykaushik » Fri, 30 Nov 2007 04:06:45 GMT

Hi All,
Thanks for your suggestions. There is another method that I tried and it
works. Since my two data sets are identical but types. So I added them
together as a one big file and created dummy based on type. Then I run OLS
and also added another line in my OLS regression:

test intercept = intercept+d;
F value of this tells whether the two intercepts are ststistically
different.


Statistical test for difference between two numbers

by HERMANS1 » Fri, 30 Nov 2007 04:58:37 GMT

The test you are proposing should, it seems to me, compare F values (or
better indicators of model fit) of the model that includes the variable
d and the model that doesn't. If omitting d does not reduce model fit,
then pooling data will not reduce the explanatory or predictive power of
the model.

Rejecting or failing to reject the null hypothesis of that test won't
make estimates or predictions of the model any less biased or estimate
the variance or prediction of the model any more accurately. No matter
how many sightings you take from a single point, or whether sighted to
one side or another, a telescope won't let you see what's behind a barn.
S
-----Original Message-----
From: XXXX@XXXXX.COM [mailto: XXXX@XXXXX.COM ]
On Behalf Of Abhay Kaushik
Sent: Thursday, November 29, 2007 3:07 PM
To: XXXX@XXXXX.COM
Cc: Abhay Kaushik
Subject: Re: Statistical test for difference between two numbers


Hi All,
Thanks for your suggestions. There is another method that I tried and it
works. Since my two data sets are identical but types. So I added them
together as a one big file and created dummy based on type. Then I run
OLS and also added another line in my OLS regression:

test intercept = intercept+d;
F value of this tells whether the two intercepts are ststistically
different.


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