Augmented Dickey-Fuller test null rejected. AR(1) in ARCH(1) p-value of 0.000

#1
Hello,
I am investigating if the comovement of the green bond market and other markets has changed pre covid-19 and during Covid-19. The plan is to use ARCH/GARCH on the logged returns of the respective marekts to attain their volatility over time. Then I will use dynamic condidional correlation on the vector of volatility to attain the comovement over time.

To the problem :
When running the the Augmented Dickey-Fuller (ADF) tests, the p-value is 0.000 for all respective markets regardless if the ADF includes 1)constant, 2) drift and constant or 3) neither constant or drift. Thus, we should be pretty sure that the time series of the respective markets aren't autoregressive. However, when running the ARCH(1) model for the respective markets, the p-value of the AR(1) parameter is close to 0.000 for all markets (see Table.1 for example). Since this is weird, I also tested to do ARMA(1,0) models for the respective marekts, in which the AR(1) is close to 0.000 (see Table.2 for example.)

Question:
1) How is it that the ADF tests p-value is 0.0000 and the AR(1) in the ARCH(1)/ARMA(1,0) also has a p-value of 0.000?
2) All parameters of the markets' ARCH model, including the ARCH effect, i.e. 1 lag residual^2, are highly significant. Since the model's parameters are significant, can I still use the model even though it is not in line with the results of the ADF?

I cannot stress how much I would appreciate any help regarding these questions!


P.S.
Here is some information that might be relevant to the question (due to the lack of statisitcal knowladge, I don't know if it is relevant.):
- The Ljung-Box test is significant for the logged returns of the respective markets. Thus, we can assume that the time series are autocorrelated. My interpretation of this is that the time series is dependent on its previous error terms, a phenomenon which should not have that much of importance to whether they are autoregressive (AR) or not.
- The PACF correlogram does show large spikes for some lags. An observation which indicates that the time series are autoregressive. Meaning that the PACF aren't in line with the results of the ADF (see Table 3. for example).
- The Jarque-Bera test shows that the data is far from normally distributed. The skew is not too alarming for 4 out of 5 time series. However, the kurtosis is giga-high (see Table 4. for descriptives).




Table.1 ARCH(1) of the logged returns of Treasury Bonds.



Table 2. ARMA(1,0) of the logged returns for the



Table 3. ACF, PACF and Q-statistics of Corporate Bonds Logged returns

Table 4. Descriptive Statistics of the logged returns for the 5 marekts considered in the thesis.
 

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