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rugarch gives two different results based on the same model…how is that even possible?

I run the code you provided and obtain the following results related to the external parameters:


Case 1 (x1,x2)
# x2 is second

            Estimate   Std. Error       t value  Pr(>|t|)
mxreg1  1.6724148 1.203377e-01  1.389767e+01 0.0000000
mxreg2  2.5310286 1.878833e-02  1.347128e+02 0.0000000

Case 2 (x2,x1)
# i.e. x2 is now first

mxreg1  2.5225382  0.04292725  58.7631024 0.000000e+00
mxreg2  1.6782986  0.12769622  13.1428990 0.000000e+00

Small differences in the coefficients are the result of the optimizer. There may be an issues in the
way starting parameters are being generated based on some recent input from Josh Ulrich (still to investigate) 
and related to arima0 (used to generate start parameters), but otherwise don?t see a large problem at first glance.

Alexios