Choosing Returns or Price Differences for ACF Analysis

Summary

The document asks whether percentage returns or log returns can be used instead of first differences to make a nonstationary financial price series stationary before examining its autocorrelation function. It notes that authors often fit ARMA models to returns and that the ACFs of percentage returns and simple price differences can look different.

No answer or evidence resolving the question is included. The central issue is that returns and price differences are distinct transformations, so their autocorrelation patterns need not match; whether a transformation is suitable depends on the series and the modeling goal. The document offers no data, stationarity tests, or guidance on choosing among them, so it is best read as a research question rather than a complete method.

Key ideas

• The document asks whether returns can replace first differences when transforming prices for time-series analysis.
• It observes that percentage returns and price differences can produce different autocorrelation patterns.
• It provides no answer, empirical comparison, or method for selecting a transformation.

Tags

# Do I use % return, log return or diff of prices to plot ACF?


# Do I use % return, log return or diff of prices to plot ACF?












I am reading a book on time series. To make a non-stationary series stationary, sometimes we need to difference the series. When it comes to finance, prices are non-stationary. Many authors fit ARMA models to return time series but returns are either log-return or % return which is different to simple differencing. I had a look at the ACF of % return and a simple diff and they are different.

My question is, is it valid to use percent or log return rather then diff to make a price series stationary?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.