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

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

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".)

>> 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

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

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

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

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.

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.

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.

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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