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Re: st: Guidance on matrix inversion for OLS in mata
From
Thomas Jacobs <[email protected]>
To
[email protected]
Subject
Re: st: Guidance on matrix inversion for OLS in mata
Date
Tue, 27 Apr 2010 11:34:04 -0500
Antoine,
Thanks for the reply. I caught my first error but appreciate the
suggestion as it addresses the missing values issue automatically.
Tom
On Tue, Apr 27, 2010 at 11:29 AM, Antoine Terracol
<[email protected]> wrote:
> Hi Thomas,
>
> have a look at cross() in the mata help files.
>
> invsym(cross(X,X)) produces (X'X)^-1
>
>
> Antoine
>
> On 27/04/2010 18:17, Thomas Jacobs wrote:
>>
>> Austin,
>>
>> Thanks for the reply. I guess I have no choice but to do as you
>> suggest or else rewrite the program entirely in Stata. I don't have
>> the days it always takes me to decipher how to do the stata mata data
>> transfer for this project at present. Every time I sit down to do
>> something like this I always feel it a roll of the dice. Do I go the
>> mata route and discover what should have been done in stata or go the
>> stata route and discover the opposite!
>>
>> Here is a short excerpt of the problem. I am simply trying to compute
>> x'x inverse for a 100 trading day time series of index returns and use
>> it to solve for betahat for a similar time series of firm returns
>> where the latter often has one or more missing values.
>>
>> Here are the initial steps I take in mata and will use an example with
>> no missing values:
>>
>> X=J(100,2,1)
>> X[.,2]=LnBAATreasSprd[800::899]
>> : X
>> 1 2
>> +-------------------------------+
>> 1 | 1 -.005838091 |
>> 2 | 1 -.0063325767 |
>> 3 | 1 .0100309728 |
>> 4 | 1 .0040479107 |
>> 5 | 1 .000136131 |
>> 6 | 1 .00040839 |
>> 7 | 1 -.0148075884 |
>> 8 | 1 -.0107393684 |
>> 9 | 1 -.002842935 |
>> 10 | 1 .0066983248 |
>> 11 | 1 -.0093153818 |
>> 12 | 1 -.0502348617 |
>> 13 | 1 -.0178726967 |
>> 14 | 1 .0145704737 |
>> 15 | 1 -.0073333359 |
>> 16 | 1 -.0029384219 |
>> 17 | 1 -.0095219389 |
>> 18 | 1 -.0128216762 |
>> 19 | 1 -.0150571838 |
>> 20 | 1 .005833914 |
>> 21 | 1 .0069765295 |
>> 22 | 1 .0038266596 |
>> 23 | 1 -.0067447214 |
>> 24 | 1 -.0082368711 |
>> 25 | 1 .0079292208 |
>> 26 | 1 -.0185827948 |
>> 27 | 1 -.0081839114 |
>> 28 | 1 .0103758555 |
>> 29 | 1 -.007115229 |
>> 30 | 1 -.0043146866 |
>> 31 | 1 .0007379653 |
>> 32 | 1 -.0010016384 |
>> 33 | 1 .0068858997 |
>> 34 | 1 -.0044625248 |
>> 35 | 1 .0031520503 |
>> 36 | 1 -.0554844476 |
>> 37 | 1 .0113020828 |
>> 38 | 1 .0031746107 |
>> 39 | 1 .0117888227 |
>> 40 | 1 -.0010267079 |
>> 41 | 1 .0095236665 |
>> 42 | 1 .0261100251 |
>> 43 | 1 -.0126527818 |
>> 44 | 1 -.0114778923 |
>> 45 | 1 .0066052717 |
>> 46 | 1 -.0084775724 |
>> 47 | 1 -.0032715374 |
>> 48 | 1 -.0015591006 |
>> 49 | 1 .0142634539 |
>> 50 | 1 .0003712231 |
>> 51 | 1 -.0077179475 |
>> 52 | 1 .0082479911 |
>> 53 | 1 .0071813553 |
>> 54 | 1 .0058756177 |
>> 55 | 1 -.0082988022 |
>> 56 | 1 -.0003692649 |
>> 57 | 1 -.0046538925 |
>> 58 | 1 -.0049419519 |
>> 59 | 1 .0040403828 |
>> 60 | 1 -.0099174296 |
>> 61 | 1 .0231989622 |
>> 62 | 1 -.0097859399 |
>> 63 | 1 -.0028060512 |
>> 64 | 1 -.0028140107 |
>> 65 | 1 .0092088645 |
>> 66 | 1 .0032609063 |
>> 67 | 1 .0080019441 |
>> 68 | 1 .0002604046 |
>> 69 | 1 .0027563504 |
>> 70 | 1 -.0134371053 |
>> 71 | 1 .0051452187 |
>> 72 | 1 .0188821666 |
>> 73 | 1 .0129679879 |
>> 74 | 1 .0097926175 |
>> 75 | 1 .0015559109 |
>> 76 | 1 -.0006521898 |
>> 77 | 1 .0055551799 |
>> 78 | 1 .0016954662 |
>> 79 | 1 0 |
>> 80 | 1 -.0011965502 |
>> 81 | 1 -.0123975417 |
>> 82 | 1 .0008581794 |
>> 83 | 1 .0113398973 |
>> 84 | 1 -.0044504236 |
>> 85 | 1 -.0101748193 |
>> 86 | 1 .0006073291 |
>> 87 | 1 .0028294155 |
>> 88 | 1 -.0016158026 |
>> 89 | 1 -.009393123 |
>> 90 | 1 -.0073215333 |
>> 91 | 1 .0056367237 |
>> 92 | 1 -.0044041635 |
>> 93 | 1 .0046085101 |
>> 94 | 1 .0162160564 |
>> 95 | 1 .0047139199 |
>> 96 | 1 -.0005505134 |
>> 97 | 1 .0033981025 |
>> 98 | 1 .034180887 |
>> 99 | 1 -.0102245966 |
>> 100 | 1 -.0060580331 |
>> +-------------------------------+
>>
>> and the inverse step with a partial excerpt (all values are zero save
>> for three cells):
>> : invsym(X*X')
>> [symmetric]
>> 1 2 3 4
>> 5
>>
>> +----------------------------------------------------------------------------
>> 1 | 0
>> 2 | 0 0
>> 3 | 0 0 0
>> 4 | 0 0 0 0
>> 5 | 0 0 0 0
>> 0
>> 6 | 0 0 0 0
>> 0
>> 7 | 0 0 0 0
>> 0
>> 8 | 0 0 0 0
>> 0
>> 9 | 0 0 0 0
>> 0
>> 10 | 0 0 0 0
>> 0
>> 11 | 0 0 0 0
>> 0
>> 12 | 0 0 0 0
>> 0
>> 13 | 0 0 0 0
>> 0
>> 14 | 0 0 0 0
>> 0
>> 15 | 0 0 0 0
>> 0
>> 16 | 0 0 0 0
>> 0
>> 17 | 0 0 0 0
>> 0
>> 18 | 0 0 0 0
>> 0
>> 19 | 0 0 0 0
>> 0
>> 20 | 0 0 0 0
>> 0
>> 21 | 0 0 0 0
>> 0
>> 22 | 0 0 0 0
>> 0
>> 23 | 0 0 0 0
>> 0
>> 24 | 0 0 0 0
>> 0
>> 25 | 0 0 0 0
>> 0
>> 26 | 0 0 0 0
>> 0
>> 27 | 0 0 0 0
>> 0
>> 28 | 0 0 0 0
>> 0
>> 29 | 0 0 0 0
>> 0
>> 30 | 0 0 0 0
>> 0
>> 31 | 0 0 0 0
>> 0
>> 32 | 0 0 0 0
>> 0
>> 33 | 0 0 0 0
>> 0
>> 34 | 0 0 0 0
>> 0
>> 35 | 0 0 0 0
>> 0
>> 36 | 0 0 0 0
>> 0
>> 37 | 0 0 0 0
>> 0
>> 38 | 0 0 0 0
>> 0
>> 39 | 0 0 0 0
>> 0
>> 40 | 0 0 0 0
>> 0
>>
>> qrinv gives something similar with a few more non-zero values while
>> cholinv and luinv produce nulls. pinv does work in this case.
>> Suffice it to say I have no problem regressing a similar single firm
>> return series on this index for the time period in question using
>> regress.
>>
>> If I am missing something, please let me know. Otherwise, I guess I
>> need to go to stata or do a better job of reproducing regress! Thanks
>> again.
>>
>> Tom
>> On Tue, Apr 27, 2010 at 10:23 AM, Austin Nichols
>> <[email protected]> wrote:
>>>
>>> Thomas Jacobs<[email protected]>:
>>> Zero is not a problem, but you should expunge the missings first;
>>> however you seem to be trying to rewrite -regress- as you go, which is
>>> far from a good idea. Why *not* export your vectors to Stata and run
>>> -regress- and let Stata handle the sample selection and matrix
>>> inversion for you?
>>>
>>> Maybe if you give us a simple example with real numbers, the problem
>>> will be clearer and you can get better guidance...
>>>
>>> On Tue, Apr 27, 2010 at 12:45 AM, Thomas Jacobs<[email protected]>
>>> wrote:
>>>>
>>>> Hi,
>>>>
>>>> I am trying to perform a lengthy series of simulations to examine some
>>>> event study methodologies. I have moved to mata for the bulk of the
>>>> work but find that for those cases where I wish to use a market model
>>>> approach requiring an OLS regression to establish abnormal returns I
>>>> am unable to generate an inverse for x'x in seeking to solve for beta
>>>> hat. I am typically working with vectors that have 1. missing values,
>>>> 2. zero values, and 3. very small values close to zero (within a
>>>> couple of decimal places such as -.01 or .005). I have tried mata's
>>>> cholinv, invsym, pinv, luinv, and qrinv (I realize that some of these
>>>> are probably inappropriate for my problem but I am no expert) and
>>>> generally get an inverse matrix of missing values or bizarre results
>>>> like a single populated row.
>>>>
>>>> I would prefer not to go back and forth between stata and mata to use
>>>> the stata regress function unless that is the only way to accomplish
>>>> this effort.
>>>>
>>>> Can anyone offer general guidance on how to proceed here? Thanks.
>>>>
>>>> Tom
>>>
>>> *
>>> * For searches and help try:
>>> * http://www.stata.com/help.cgi?search
>>> * http://www.stata.com/support/statalist/faq
>>> * http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>> --
>> Thomas Jacobs
>>
>> *
>> * For searches and help try:
>> * http://www.stata.com/help.cgi?search
>> * http://www.stata.com/support/statalist/faq
>> * http://www.ats.ucla.edu/stat/stata/
>>
>
> --
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> pour des virus ou des polluriels et rien de
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>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
--
Thomas Jacobs
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/