Solved – Testing heteroscedasticity in seasonal ARIMA model


I have estimated seasonal ARIMA(1,2,1)x(0,0,2) and then to test for heteroscedasicity transformed it to lm object with

x <- lm(residuals(m) ~ 1), with m = auto.arima(ts.loggdpq,stepwise=FALSE)
and ts.loggdpq is quaterrly, logged gdp data.

Testing for heteroscedasicity with bptest(x) resulted with

        studentized Breusch-Pagan test

data:  x BP = 3.429e-30, df = 0, p-value < 2.2e-16

meaning that I can't reject the null hypothesis. Does this mean that my model is not effective? Should I transform it to ARCH(q) model?

Best Answer

Your $p$-value is very small, so you actually will reject the null hypothesis at any sensible significance level.

(I just wonder if you are using the test correctly. Are you supplying any explanatory variables for the test? Why do you have zero degrees of freedom there: df=0?)

However, BP test does not test for ARCH patterns. It tests for another kind of heteroskedasticity: that the magnitude of errors (measured by squared errors) varies with the explanatory variables in the model (see Wikipedia for more details).

Meanwhile, ARCH is autoregressive behaviour in squares of errors, which is quite different from the above. Therefore, ARCH structure in model errors is not an implication of the test result.