Using the ADL (1,1) Regression $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + \gamma _ { 1 } X _ { t - 1 } + u _ { t }$

question 6

Multiple Choice

Using the ADL (1,1) regression $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + \gamma _ { 1 } X _ { t - 1 } + u _ { t }$
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) \(\sigma _ { t } ^ { 2 } = u _ { t - 1 } ^ { 2 } + \ldots + u _ { t - p } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }\)
• C) \(\sigma _ { t } ^ { 2 } = \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }\)
• D) \(\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }\)

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