Suppose I have one time series and two competing models that describe it. Model 1 is ARMA$(p_1,q_1)$, model 2 is ARMA$(p_2,q_2)$-GARCH$(r,s)$.

I obtain AIC values of model 1 and model 2. I would like to conclude that the model with the lower AIC value is the prefered model. However, I am not sure whether I can compare AIC values coming from two different classes of models such as ARMA and ARMA-GARCH.

My intuition is the following: if we find a model that nests both model 1 and model 2, we should be able to use AIC to compare the former two. Indeed, ARMA$(p_1,q_1)$ and ARMA$(p_2,q_2)$-GARCH$(r,s)$ are both nested within ARMA$(\max\{p_1,p_2\},\max\{q_1,q_2\})$-GARCH$(r,s)$ and may be obtained from the latter model by applying zero restrictions on coefficients.

However, I am not sure whether my approach makes sense. Could someone please elaborate on this issue and answer the question: can we, or can we not, use AIC to compare ARMA models with ARMA-GARCH models?

Suppose I have one time series and two competing models that describe it. Model 1 is ARMA$(p_1,q_1)$, model 2 is ARMA$(p_2,q_2)$-GARCH$(r,s)$.

I obtain AIC values of model 1 and model 2. I would like to conclude that the model with the lower AIC value is the prefered model. However, I am not sure whether I can compare AIC values coming from two different classes of models such as ARMA and ARMA-GARCH.

My intuition is the following: if we find a model that nests both model 1 and model 2, we should be able to use AIC to compare the former two. Indeed, ARMA$(p_1,q_1)$ and ARMA$(p_2,q_2)$-GARCH$(r,s)$ are both nested within ARMA$(\max\{p_1,p_2\},\max\{q_1,q_2\})$-GARCH$(r,s)$ and may be obtained from the latter model by applying zero restrictions on coefficients.

However, I am not sure whether my approach makes sense. Could someone please elaborate on this issue and answer the question: can we, or can we not, use AIC to compare ARMA models with ARMA-GARCH models?

Suppose I have one time series and two competing models that describe it. Model 1 is ARMA(p1,q1), model 2 is ARMA(p2,q2)-GARCH(r,s).
I obtain AIC values of model 1 and model 2.
I would like to conclude that the model with the lower AIC value is the prefered model.
However, I am not sure whether I can compare AIC values coming from two different classes of models such as ARMA and ARMA-GARCH.

My intuition is the following: if we find a model that nests both model 1 and model 2, we should be able to use AIC to compare the former two. Indeed, ARMA(p1,q1) and ARMA(p2,q2)-GARCH(r,s) are both nested within ARMA(max{p1,p2},max{q1,q2})-GARCH(r,s) and may be obtained from the latter model by applying zero restrictions on coefficients.

However, I am not sure whether my approach makes sense. Could someone please elaborate on this issue and answer the question: can we, or can we not, use AIC to compare ARMA models with ARMA+GARCH models?

Suppose I have one time series and two competing models that describe it. Model 1 is ARMA$(p_1,q_1)$, model 2 is ARMA$(p_2,q_2)$-GARCH$(r,s)$.

I obtain AIC values of model 1 and model 2. I would like to conclude that the model with the lower AIC value is the prefered model. However, I am not sure whether I can compare AIC values coming from two different classes of models such as ARMA and ARMA-GARCH.

My intuition is the following: if we find a model that nests both model 1 and model 2, we should be able to use AIC to compare the former two. Indeed, ARMA$(p_1,q_1)$ and ARMA$(p_2,q_2)$-GARCH$(r,s)$ are both nested within ARMA$(\max\{p_1,p_2\},\max\{q_1,q_2\})$-GARCH$(r,s)$ and may be obtained from the latter model by applying zero restrictions on coefficients.

However, I am not sure whether my approach makes sense. Could someone please elaborate on this issue and answer the question: can we, or can we not, use AIC to compare ARMA models with ARMA-GARCH models?