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: