# Alternative to Chow test in the case of heavy tailed residual distribution

I would like to check if two subpopulations of my data have the same parameters in a model. Model 1 is based on subpopulation 1 and Model 2 is based on subpopulation 2.

Model 1: $$y=x^\alpha + \gamma +\varepsilon$$
Model 2: $$y=x^\beta+ \theta +\varepsilon$$

The parameters of the two models are estimated with Nonlinear Least Squares.

The hypothesis I want to test is therfore:

H0: $$\gamma$$ = $$\theta$$ and $$\alpha = \beta$$

Normally I would use an Chow-test/F-test to test this hypothesis. However the residuals ($$\varepsilon$$) of the two models are heavy tailed. Since the F-test is sensitive to non-normality and will probably result in small p-values I would like to use another test. What test would be suitable?

• Do you have an idea why the residuals are heavy tailed? – Martijn Weterings Jan 14 at 18:20
• Because the dependent variable is a stock return measured on a short period. – K. Roelofs Jan 14 at 18:27
• Could you explain that a bit better for statisticians that do not understand the stock exchange. I am asking this because there might be multiple ways/methods/processes that "create" residuals (residuals which is different from error terms but also for those it is interesting to know the process that causes them). – Martijn Weterings Jan 14 at 20:10