An AR(2)process is written as
A) $\varepsilon _ { t } = \rho \varepsilon _ { t - 1 } + u _ { t }$
B) $\varepsilon _ { i } = \rho \varepsilon _ { i - 1 } + u _ { i }$
C) $\varepsilon _ { t } = \rho _ { 1 } \varepsilon _ { t - 1 } + \rho _ { 2 } \varepsilon _ { t - 2 } + u _ { t }$
D) $\varepsilon _ { i } = \rho _ { 1 } \varepsilon _ { i - 1 } + \rho _ { 2 } \varepsilon _ { i - 2 } + u _ { i } .$

Question

Quizplus · Accepted Answer

An AR(2) process is written as $\varepsilon _ { t } = \rho _ { 1 } \varepsilon _ { t - 1 } + \rho _ { 2 } \varepsilon _ { t - 2 } + u _ { t }$. Therefore, the best choice is C, as it represents the correct form of an AR(2) process. The other choices, A and B, only have one lagged term and do not represent an AR(2) process. Choice D has the correct form but uses i instead of t as the time index, which is a subtle difference but could cause confusion.

An AR(2)process Is Written as A) εt=ρεt−1+ut\varepsilon _ { t } = \rho \varepsilon _ { t - 1 } + u _ { t }εt​=ρεt−1​+ut​

An AR(2)process Is Written as
A) $\varepsilon _ { t } = \rho \varepsilon _ { t - 1 } + u _ { t }$