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?

  • $\begingroup$ Do you have an idea why the residuals are heavy tailed? $\endgroup$ – Sextus Empiricus Jan 14 '19 at 18:20
  • $\begingroup$ Because the dependent variable is a stock return measured on a short period. $\endgroup$ – K. Roelofs Jan 14 '19 at 18:27
  • $\begingroup$ 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). $\endgroup$ – Sextus Empiricus Jan 14 '19 at 20:10

If you extend your model to include Intervention Variables your residuals will be free of the "fat tails " This will enable you to perform the CHOW Test . See Can I modify the Chow Statistic for use with ARIMAx models? for a similar discussion and my comments on extending the test . The comments apply to not only alowing for arima coefficients BUT empirically identified intervention variables ( to enable non-fat error distributions )

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