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# Re: st: Running Product Function

 From Yuval Arbel To statalist@hsphsun2.harvard.edu Subject Re: st: Running Product Function Date Mon, 10 Dec 2012 00:41:41 +0200

```So maybe I could try the harmonic mean as well.

P.S. The geometric mean is excellent for my objectives:
psychologically if there is a positive momentum it is plausible that
more weight is given to the latter periods, while if there is a
negative momentum more weight is given to earlier periods (where the
market was high)

On Mon, Dec 10, 2012 at 12:25 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
> Thanks Nick. That was very helpful.
>
> On Mon, Dec 10, 2012 at 12:14 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>> Note also that the geometric mean of this series is 25. This implies
>> that while the arithmetic mean gives more weight to earlier periods,
>> the geometric mean gives more weight to latter periods.:
>>
>>  ameans(reduct_per)if appt==2862
>>
>>     Variable |    Type        Obs        Mean       [95% Conf. Interval]
>> -------------+----------------------------------------------------------
>>   reduct_per | Arithmetic      37    8.108108        4.152295   12.06392
>>              |  Geometric      12          25              25         25
>>              |   Harmonic      12          25              25         25
>> ------------------------------------------------------------------------
>>
>>
>>
>> On Mon, Dec 10, 2012 at 12:06 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>> Eventually, I improved the system and put:the following commands:
>>>
>>> by appt: replace reduct_per=1 if reduct_per==0
>>> by appt: gen y1=exp(sum(ln(reduct_per)))
>>>
>>> I got the following table, which is exactly what I need (I don't want
>>> the geometric mean to be set to zero):
>>>
>>> . list reduct_per y3 if appt==2862
>>>
>>>         +---------------------+
>>>         | reduct~r         y3 |
>>>         |---------------------|
>>>     30. |        1          1 |
>>>     31. |        1          1 |
>>>     32. |        1          1 |
>>>     33. |        1          1 |
>>>     34. |        1          1 |
>>>         |---------------------|
>>>     35. |        1          1 |
>>>     36. |        1          1 |
>>>     37. |        1          1 |
>>>     38. |        1          1 |
>>>     39. |        1          1 |
>>>         |---------------------|
>>>     40. |        1          1 |
>>>     41. |        1          1 |
>>>     42. |        1          1 |
>>>     43. |        1          1 |
>>>     44. |        1          1 |
>>>         |---------------------|
>>>     45. |        1          1 |
>>>     46. |        1          1 |
>>>     47. |        1          1 |
>>>     48. |        1          1 |
>>>     49. |        1          1 |
>>>         |---------------------|
>>>     50. |        1          1 |
>>>     51. |        1          1 |
>>>     52. |        1          1 |
>>>     53. |        1          1 |
>>>     54. |        1          1 |
>>>         |---------------------|
>>>     55. |       25         25 |
>>>     56. |       25        625 |
>>>     57. |       25      15625 |
>>>     58. |       25     390625 |
>>>     59. |       25    9765625 |
>>>         |---------------------|
>>>     60. |       25   2.44e+08 |
>>>     61. |       25   6.10e+09 |
>>>     62. |       25   1.53e+11 |
>>>     63. |       25   3.81e+12 |
>>>     64. |       25   9.54e+13 |
>>>         |---------------------|
>>>     65. |       25   2.38e+15 |
>>>     66. |       25   5.96e+16 |
>>>         +---------------------+
>>>
>>>
>>> On Sun, Dec 9, 2012 at 11:56 PM, Nick Cox <njcoxstata@gmail.com> wrote:
>>>> That is reasonable if and only if zero is in effect a code for missing
>>>>
>>>> (In terms of your earlier reference, -prod()- is a user-written -egen-
>>>> function which must be installed from
>>>>
>>>> STB-51  dm71  . . . . . . . . . . . .  Calculating the product of observations
>>>>         (help prod if installed)  . . . . . . . . . . . . . . . . . .  P. Ryan
>>>>         9/99    pp.3--4; STB Reprints Vol 9, pp.45--48
>>>>         extension to egen for producing the product of observations
>>>>
>>>> Please remember to explain _where_ you obtained user-written code.)
>>>>
>>>> Nick
>>>>
>>>> On Sun, Dec 9, 2012 at 9:40 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>>>> I don't have negative values, but I have zeros, in which case I can
>>>>> replace them by one and then take the -ln()-
>>>>>
>>>>> On Sun, Dec 9, 2012 at 11:31 PM, Nick Cox <njcoxstata@gmail.com> wrote:
>>>>>> Oddly enough I was thinking earlier today about how you would
>>>>>> generalise this if any values were not positive.
>>>>>>
>>>>>> If any value is zero, then the product becomes zero; otherwise one
>>>>>> would need to separate out products of -abs()- and -sign()-.
>>>>>>
>>>>>> Nick
>>>>>>
>>>>>> On Sun, Dec 9, 2012 at 9:19 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>>>>>
>>>>>>> Please ignore my previous e-mails regarding this question
>>>>>>>
>>>>>>> After a short additional search, I found a very nice (and well known)
>>>>>>> trick proposed by Nick Cox to address the problem (which, from some
>>>>>>> reason did not come to my mind):
>>>>>>>
>>>>>>> bysort group : gen prod = sum(ln(x))
>>>>>>> by group : replace prod = exp(prod[_N])
>>>>>>>
>>>>>>> On Sun, Dec 9, 2012 at 11:05 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>>>>>>> P.S. According to stata's help, the details of the author of the
>>>>>>>> -prod()- function is:
>>>>>>>>
>>>>>>>> Philip Ryan
>>>>>>>> Department of Public Health
>>>>>>>> South Australia
>>>>>>
>>>>>>
>>>>>> On Sun, Dec 9, 2012 at 10:53 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>>>>>
>>>>>>>>> I appreciate very much your assistance in the following question:,
>>>>>>>>>
>>>>>>>>> I'm looking for an equivalent function for -gen y1=sum()- which will
>>>>>>>>> calculate running product for each point in time
>>>>>>>>>
>>>>>>>>> In fact, what I would like to calculate is a running geometric mean
>>>>>>>>>
>>>>>>>>> Note also that -gen y2=prod()- does not work (i.e., stata does not
>>>>>>>>> identify the function). Only -egen y2=prod()- works, but it generates
>>>>>>>>> only one product for each panel, and this is not what I need.
>>>>>>>>>
>>>>>>>>> Finally, I tried the -amean- command,, but it simply gives summary
>>>>>>>>> statistics of different means, and it is not a function..
>>>> *
>>>> *   For searches and help try:
>>>> *   http://www.stata.com/help.cgi?search
>>>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>
>>>
>>>
>>> --
>>> Dr. Yuval Arbel
>>> 4 Shaar Palmer Street,
>>> Haifa 33031, Israel
>>> e-mail1: yuval.arbel@carmel.ac.il
>>> e-mail2: yuval.arbel@gmail.com
>>
>>
>>
>> --
>> Dr. Yuval Arbel
>> 4 Shaar Palmer Street,
>> Haifa 33031, Israel
>> e-mail1: yuval.arbel@carmel.ac.il
>> e-mail2: yuval.arbel@gmail.com
>
>
>
> --
> Dr. Yuval Arbel
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1: yuval.arbel@carmel.ac.il
> e-mail2: yuval.arbel@gmail.com

--
Dr. Yuval Arbel