2

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?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
K. Roelofs
  • 333
  • 1
  • 11
  • Do you have an idea *why* the residuals are heavy tailed? – Sextus Empiricus Jan 14 '19 at 18:20
  • Because the dependent variable is a stock return measured on a short period. – K. Roelofs Jan 14 '19 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). – Sextus Empiricus Jan 14 '19 at 20:10

1 Answers1

1

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 )

IrishStat
  • 27,906
  • 5
  • 29
  • 55