Such skewed, thick-tailed data suggest a model with multiplicative errors instead of additive errors. A standard solution is to transform the dependent variable by taking the natural logarithm.
Can anyone explain multiplicative errors and additive errors here?
Many thanks in advance!
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$\begingroup$There is not enough context here, but here is a general explanation:
Let's say you are trying to measure an underlying signal $X$ and the observed signal $Y$ is related to the actual signal by $Y = f(X) + \epsilon$, where $f(\cdot)$ is some function (either known or estimated) and $\epsilon$ is the measurement error or noise. In this case, the error is additive, because it adds to the model $Y = f(X)$.
In an alternative scenario, consider that $Y$ and $X$ are related by $Y = g(X)\epsilon$. In this case, the error term $\epsilon$ is multiplicative, because it multiplies with the model $Y = g(X)$. By applying the log transformation $\log(Y) = \log(g(X)) + \log(\epsilon)$, we are back to an additive error framework.
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