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I am fitting models to stock price time series. The interval of each series is 40-minutes (relatively small time frames, in the context of stocks). I will use ARIMA or GARCH in R. Purpose of project is detecting a structural change point in the data (no forecasting).

Is is defensible to claim that as the time interval in question gets smaller, the use of log returns [ diff(log(stock$price)) ] has few disadvantages while retaining its advantages?

For example, one reason in favor of using log returns is that a drop of 10 cents between minute 2 and minute 3 might be more/less significant than a drop of 10 cents between minutes 32 and 33. Using log returns provides a common scale.

However, one not unreasonable alternative would be to normalize the dataset by dividing by the initial price in the series. Then all points in the series would reflect percentage differences from the first point.

See these two explanations of the use of log returns:

https://quantivity.wordpress.com/2011/02/21/why-log-returns/

https://mathbabe.org/2011/08/30/why-log-returns/

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    $\begingroup$ What is the context of the question? In which sense do you mean "more sound"? More sound than what? What alternatives are you considering? What is the purpose of your analysis? $\endgroup$ – Richard Hardy Jun 30 '17 at 10:09
  • $\begingroup$ It's mentioned in one of your links that the first order Taylor approximation $\log(1+r) \approx r$ (where $r$ is the percentage return) is more accurate for small returns. So if by interval you mean the entire window of your time series, it might not be a big deal for you. They might be overwhelmingly close to each other $\endgroup$ – Taylor Jun 30 '17 at 21:58

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