I computed an ARMA model for conditional mean on a financial time series of log returns. The model that minimise the AIC was an ARMA(5,5) and all but 2 of the coefficients ( AR $\phi_4$ and MA $\theta_4$) resulted statistical significant. The ACF looked cleaned out. The ACF of squared residuals seems autocorrelated.
However, after implementing an ARMA(5,5)-GARCH(1,1) to model also conditional variance and get rid of heteroskedasticity, the estimated $\omega$, $\alpha_1$ and $\beta_1$ were statistical significant, but now all the arma coefficient (but $\phi_5$ at 10% level) turned out to be non-significant now.
- What's going on? How would you comment the results?
- I was refusing the the weak form of the Efficient Market Hypothesis (EMH) on the basis of the significativity of the ARMA coefficient estimates. Indeed past returns were found to have an effect on future returns. But now the results from GARCH say the opposite. Who's right? Could I still reject EMH or should I revise my hypothesis?