# in time series analysis or finance people use log return for inference but returns can take negative value [closed]

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

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.