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in time series analysis or finance people use log return for inference but returns can take negative value. but log cant take negative values. so why we use it when log is not defined on most of values

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It is not negative returns that are an issue.

Assume the following prices in two periods: $P_o = 100$ ; $P_1 = 99$
Standard percent calc: $$\frac{P_1}{P_0}-1 = -0.01$$ which is -1% . Using the natural logarithm you get $$ln(99)-ln(100) = -0.01005$$ which is essentially identical.

Negative prices are an issue - but these are not observed for many economic variables like stock prices etc. For a general discussion about logs, you can have a look at this. It also discusses this calculation here in more detail.

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