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I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?

Here is the (G)ARCH(p, q) process

$\sigma_t^2 = \underbrace{ \underbrace{ \alpha_0 + \sum_{i=1}^q \alpha_ir_{t-i}^2} _{ARCH} + \sum_{i=1}^p\beta_i\sigma_{t-i}^2} _{GARCH}$

And here is the ARMA(p, q):

$ X_t = c + \varepsilon_t + \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \varepsilon_{t-i}.\,$

Is the ARMA simply an extension of the GARCH, GARCH being used only for returns and with the assumption $r = \sigma\varepsilon$ where $\varepsilon$ follows a strong white process?

I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?

Here is the (G)ARCH(p, q) process

$$\sigma_t^2 = \underbrace{ \underbrace{ \alpha_0 + \sum_{i=1}^q \alpha_ir_{t-i}^2} _{ARCH} + \sum_{i=1}^p\beta_i\sigma_{t-i}^2} _{GARCH}$$

And here is the ARMA($p, q$):

$$ X_t = c + \varepsilon_t + \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \varepsilon_{t-i}.\,$$

Is the ARMA simply an extension of the GARCH, GARCH being used only for returns and with the assumption $r = \sigma\varepsilon$ where $\varepsilon$ follows a strong white process?

I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?

Here is the (G)ARCH(p, q) process

$\sigma_t^2 = \underbrace{ \underbrace{ \alpha_0 + \sum_{i=1}^q \alpha_ir_{t-i}^2} _{ARCH} + \sum_{i=1}^p\beta_i\sigma_{t-i}^2} _{GARCH}$

And here is the ARMA(p, q):

$ X_t = c + \varepsilon_t + \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \varepsilon_{t-i}.\,$

Is the ARMA simply an extension of the GARCH? GARCH being used only for returns and with the assumption $r = \sigma\varepsilon$ where $\varepsilon$ follows a strong white process.

I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?

Here is the (G)ARCH(p, q) process

$\sigma_t^2 = \underbrace{ \underbrace{ \alpha_0 + \sum_{i=1}^q \alpha_ir_{t-i}^2} _{ARCH} + \sum_{i=1}^p\beta_i\sigma_{t-i}^2} _{GARCH}$

And here is the ARMA(p, q):

$ X_t = c + \varepsilon_t + \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \varepsilon_{t-i}.\,$

Is the ARMA simply an extension of the GARCH, GARCH being used only for returns and with the assumption $r = \sigma\varepsilon$ where $\varepsilon$ follows a strong white process?