O que é Autoregressive, moving-average and ARMA processes?

With $(\varepsilon_t)$ white noise of variance $\sigma^2$: an autoregressive process of order $p$, AR($p$), satisfies $X_t = c + \sum_{i=1}^p\phi_iX_{t-i} + \varepsilon_t$; a moving-average process of order $q$, MA($q$), is $X_t = \mu + \varepsilon_t + \sum_{j=1}^q\vartheta_j\varepsilon_{t-j}$; an ARMA process combines them, $\phi(L)X_t = c + \vartheta(L)\varepsilon_t$ with $\phi(z) = 1 - \sum_i\phi_iz^i$, $\vartheta(z) = 1 + \sum_j\vartheta_jz^j$ and $L$ the lag operator.