Model time series as real-valued or integer-valued?

Question

I have a positive-valued time series of daily prices (a sample is listed below -- there are a few thousand observations) that is recorded to two decimal places. It is stationary after computing the fractional change y(t) = x(t)/x(t-1) - 1. The standard deviation of changes is small enough that often the change is exactly zero. Should I fit the usual ARMA model with normal errors to fractional changes or fit an integer-valued ARMA model to the first differences? There are many software packages for ARMA models with normal errors. What software exists for integer-valued ARMA models? When is it necessary to fit an integer-valued ARMA model?

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Answer 1

two things come to mind ...

1. if a series is non-stationary this may be remedied by suitable differencing or suitable de-meaning see What "more" does differencing (d>0) do in ARIMA than detrend? for more . Unwarranted differencing can unfortunately inject structure.

2. If you multiply (scale) your data by 100 ..the problem vanishes. Note that the classic time series example was the airline series which is in integers.
   https://autobox.com/cms/index.php/blog/entry/u-didnt-need-logs details the data set.

The real problem has nothing to do with integers BUT all to do with low count discrete data e.g. 1.1.2.1.0.2.1.0.0.1.0.1.0.1 having just three different values. I have found that if there are more than 7-8 kinds of values ARIMA model identification can be useful but that's just a "rule of thumb" .

We then take the forecast and integerize it so as to have it compatible with the observed data.