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# Re: st: Slope of a univariate time series

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Slope of a univariate time series Date Sat, 9 Jun 2012 17:13:21 +0100

```On your thoughts

1. I think you are confusing fitting a Poisson distribution with
Poisson regression, which is a much more general procedure. This may
be because you have not yet read the documentation for -poisson- or
any of the supporting references.

3. This is a matter of taste. My own taste is that if the idea of an
overall slope makes sense then it makes sense to estimate it with a
model. The slope between neighbouring data points may seem closer to
the data but it is in fact more sensitive to individual errors.
Testing whether slopes are genuine (meaning, not zero) is a problem
that has served as a sandpit for mathematical statisticians, but data
analysts in my experience are usually happy to settle the question
from a plot of the data.

At a wild guess the most common decay rate problems are those of
exponential or power-law declines, which are most commonly regarded as
regression problems. The time series aspect of the data is quite
secondary. When particular functions arise in theoretical discussions
or are customary in the literature (e.g. exponential decay to a
positive asymptote) then often -nl- is needed.

The problem with a straight linear regression fitted to a declining
series is that it predicts negative values beyond some finite time,
which usually makes neither theoretical or practical sense whenever
what is being measured is a count or amount. This doesn't bite with
Poisson regression, but that nice property does not guarantee that
Poisson regression is what you need.

All that said, the data you posted in
http://www.stata.com/statalist/archive/2012-06/msg00486.html are not
even approximately linearized by thinking in terms of log(hits), as a
plot shows. So you may need some special-purpose model.

Nick

On Sat, Jun 9, 2012 at 2:37 PM, Tashi Lama <ltashi32@hotmail.com> wrote:
> Three thoughts
> 1. I have never looked at any distribution as a measure to find slope or rate for that matter. I looked distribution more of finding probability, mean and deviation. How it generates slope is sth i need to go back and do some reading but i do see that the data spread in my dataset resembles that of a poisson.
> 2. I was actually thinking of running regression which will give me "beta" which is a slope mathematically. But i suspect that would be a overkill. Honestly, i don't even know i use regression although mathematically speaking it could.
> 3. May be i can find slope at each two consecutive data points and find median or mean.
>
> In any case, what is the most common way of finding slope or a decay rate in a univariate time series in stata?

On Jun 9, 2012, at 9:11 AM, Nick Cox <njcoxstata@gmail.com> wrote:

>> Yes, but Tashi's context implies that linear decline is not a good
>> model. I earlier recommended Poisson regression, for which see
>> -poisson-.

On Sat, Jun 9, 2012 at 2:00 PM, Muhammad Anees <anees@aneconomist.com> wrote:
>>> Do you mean d(x)/d(t)?
>>> Then I guess simple OLS will do that
>>>
>>> reg x t
>>> b is the slope then assuming above.
>>
>> On Sat, Jun 9, 2012 at 5:51 PM, Tashi Lama <ltashi32@hotmail.com> wrote:
>>
>>>>  Is there a stata command or a module to find the slope of a univariate time series?

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