# Significance of return under stable distribution

if I want to use t-test to test significance of my returns, it assumes the random variable is distributed normally. But in my work I work under stable distributed returns. It seems inappropriate to use this test then. Is there an alternative? Cannot google anything.

Cheers guys

• Using 'I'm Feeling Lucky' button: tandfonline.com/doi/abs/10.1080/02664763.2012.740618 Parkinson (2102) z Test for the significance of the mean of a stable probability distribution – noob2 Sep 7 '16 at 19:38
• Thanks a lot @noob2 , exactly what I wanted. Guess should have searched z test :) Want to copy it as answer so I can accept it? Thanks a lot again! – Jan Sila Sep 8 '16 at 14:13

I am not an expert on this topic, but I saw a recent article

Parkinson (2102): z Test for the significance of the mean of a stable probability distribution http://tandfonline.com/doi/abs/10.1080/02664763.2012.740618

that may be of interest to you.

The four parameters of a stable distribution may be estimated by maximum likelihood. John Nolan's stable package is available from http://www.robustanalysis.com/ in forms suitable for use in C, C++, R, matlab Mathematica and excel with Windows, Linux or Mac. The package estimates the parameters and produces confidence intervals.

You might also look at the stable.exe program available at http://fs2.american.edu/jpnolan/www/stable/stable.html. This also does maximum likelihood estimates of the parameters and produces confidence intervals.

You might also find some of the material in http://www.tcd.ie/Economics/staff/frainj/Stable_Distribution/thesis_main_5.pdf useful

• Thanks, I've got those. Nolan's MLE estimates are paid only, so I made my own before. I needed to test significance of non-zero mean (location parameter) for stable distributions as noob2 found in the answer above – Jan Sila Sep 14 '16 at 17:59
• The Nolan stable,exe file is free. I will try and get a copy of the Parkinson paper and see what is new. The version of the z-statistic derived from the ML estimates has been widely used and the basic theory dates back to DuMouchel in the 70's. (1971, 1973 and 1975) – user1483 Sep 15 '16 at 21:34
• I've got and implemented Parkinson's method... Will check our DuMouchel :) thanks – Jan Sila Sep 15 '16 at 21:37
• Btw exe file is good as long as your dont have a Mac :D – Jan Sila Sep 15 '16 at 21:37
• The stable.exe program is basically a simple MS-Dos program and runs in windows in a command window. I have no experience with Mac I would think that it would run on a Mac using one of the emulators used to run old Dos games – user1483 Sep 16 '16 at 21:50