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I have a time series of floating numbers, say,

0.1, 0.5, 1.1, 0.6, 2.0, 1.4, 0.4

Now, I would like to model this series with Poisson regression, since the numbers, even though they seem continuous, are in fact from a specific range/set of possible values from 0.1 to 3 in 0.1 steps: you can have 0.1 and 0.2, but not 0.15. To me it does not seem like very much different from having counts.

I used this transformation: all floats have at most 1 digit of precision limited by the equipment that makes measurements, so I simply multiply them all by 10, and get the transformed time series output of

1, 5, 11, 6, 2, 14, 4

I tried running Poisson regression on it, and frankly speaking it does as well as it did for similar quantities of counts.

What are the pitfalls of this approach? Is there any literature doing something similar?

My biggest concern is the relation of mean-to-variance in Poisson distribution. By multiplying the time series by 10, I automatically change the variance/expectation of Poisson, so the distribution changes. However, I think that that scaling does not actually influence the point prediction, only variance, since I can easily get the inverse transform of the prediction, and my practice showed it is pretty good.

How can this be justified/explained?

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marked as duplicate by kjetil b halvorsen, Peter Flom Mar 29 at 12:39

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  • $\begingroup$ 1. How do your numbers arise? 2. Discreteness, even on a lattice, is not the same thing as "having counts". 3 The Poisson has mean = variance; there seems reason to doubt this would be likely for your data. Perhaps a quasi-Poisson model would be an adequate approximation in some circumstances but even the assumption that variance is proportional to mean is not usually the case outside count data. $\endgroup$ – Glen_b Mar 20 at 15:06
  • $\begingroup$ @Glen_b, what if it is turned this way: we assume that data transformation from unknown variable results in Poisson, not that Poisson is transformed into Poisson? $\endgroup$ – SWIM S. Mar 20 at 15:12
  • $\begingroup$ @Glen_b, it is a scale, which measures weight in discrete intervals. Strictly speaking, it round to the closest value up to 1 decimal. $\endgroup$ – SWIM S. Mar 20 at 15:44
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    $\begingroup$ If the underlying variable is a weight (continuous, positive) that gets discretized, then I'd expect that variance directly proportional to mean is highly unlikely. I see no obvious basis on which to choose a Poisson or even a quasi-Poisson model $\endgroup$ – Glen_b Mar 20 at 23:46
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