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

question 41

Short Answer

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

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

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