Using the ADL(1,1)regression Y_t = ?₀ + ?₁Y_t_-₁ + $\gamma _ { 1 }$ X_t_-₁ + u_t, the ARCH model for the regression error assumes that u_t is normally distributed with mean zero and variance $\sigma _ { t } ^ { 2 }$ , where
A) $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \alpha _ { 2 } u _ { t - 2 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 }$ .
B) $\sigma _ { t } ^ { 2 } = u _ { t - 1 } ^ { 2 } + \ldots + u _ { t - p } ^ { 2 } + \varphi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }$ .
C) $\sigma _ { t } ^ { 2 } = \varphi 1 \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }$ .
D) $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 } + \varphi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }$ .

Question

Using the ADL(1,1)regression Y_t = ?₀ + ?₁Y_t_-₁ +

\gamma _ { 1 }

X_t_-₁ + u_t, the ARCH model for the regression error assumes that u_t is normally distributed with mean zero and variance

\sigma _ { t } ^ { 2 }

, where
A)

\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \alpha _ { 2 } u _ { t - 2 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 }

.
B)

\sigma _ { t } ^ { 2 } = u _ { t - 1 } ^ { 2 } + \ldots + u _ { t - p } ^ { 2 } + \varphi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }

.
C)

\sigma _ { t } ^ { 2 } = \varphi 1 \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }

.
D)

\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 } + \varphi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }

.

Quizplus · Accepted Answer

The Answer of Using the ADL(1,1)regression Y_t = ?₀ + ?₁Y_t_-₁ + $\gamma _ { 1 }$ X_t_-₁ + u_t, the ARCH model for the regression error assumes that u_t is normally distributed with mean zero and variance $\sigma _ { t } ^ { 2 }$ , where A) $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \alpha _ { 2 } u _ { t - 2 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 }$. B) $\sigma _ { t } ^ { 2 } = u _ { t - 1 } ^ { 2 } + \ldots + u _ { t - p } ^ { 2 } + \varphi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }$. C) $\sigma _ { t } ^ { 2 } = \varphi 1 \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }$. D) $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 } + \varphi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \varphi _ { q } \sigma _ { t - q } ^ { 2 }$.

Using the ADL(1,1)regression Yt = ?0 + ?1Yt-1 γ1\gamma _ { 1 }γ1​

Using the ADL(1,1)regression Y_t = ?₀ + ?₁Y_t_-₁ $\gamma _ { 1 }$