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I was fitting the NIFTY 50 Daily Log Returns (To be more precise Returns in this case refers to the Log of 1+Returns rather than Log of Returns as Log cannot be taken of negative values which returns can be) from 2013-2023 to Asymmetric Laplace Distribution and I found the closest fit to the Empirical Distribution is the ALD with these parameters:

Location (µ) = 0.13%, Scale (b) = 0.74% and Asymmetry Parameter (k) = 1.0565.

I was wondering though whether the ALD with these parameters has Finite Variance or Infinite Variance as the Wiki article on the Log-Laplace Distribution is suggesting that depending on the parameters the Log-Laplace Distribution can be infinite/finite variance.

I read the paper linked in the article which referenced this issue but I can't seem to understand what the paper is suggesting. Here is a link to the paper (Kozubowski and Podgorsky: A Log Laplace Growth Rate Model, Mathematical Scientist, vol. 28, 2003) in case interested.

Thanks for all your help,

Anon9001.

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    $\begingroup$ On p. 4 section 2.3 it states that: "Note that the mean and the variance are finite only if $\alpha > 1$ and $\alpha > 2$, respectively." I believe $\alpha$ in the paper is the location parameter (correct me if I'm wrong). $\endgroup$
    – Pleb
    Feb 9, 2023 at 20:29

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Forgot to check the Wiki page of the ALD Distribution as the Variance Formula of the ALD is there. K is the Asymmetry Parameter and Lamda is the Scale Parameter. Considering the values for the two are 1.0565 and 0.74% respectively the Variance of this Distribution is equal to 36682.89253 which I believe indicates the Variance of the ALD Distribution with these parameters is Finite.

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