Key Topics

# Key Topics - Key Topics Probability Concepts Understand and...

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Unformatted text preview: Key Topics Probability Concepts Understand and verify the following implications, with X = f x 1 ; : : : ; x n g , & E ( u t j X ) = 0 ) E ( u t j x t ) = 0 ) E ( u t ) = 0 & E ( u t j x t ) = 0 ) E ( x t u t ) = 0 You should know this from prior coursework, but it is covered in the Population Regression Models lecture Understand & f y t ; x t g t & 1 i.i.d. ) f y t ; x t g t & 1 stationary and ergodic & f y t ; x t g t & 1 i.n.i.d. ; f y t ; x t g t & 1 stationary and ergodic This concept is covered in the Ergodic Stationarity lecture Understand that if f y t ; x t g t & 1 is a stationary and ergodic sequence, then & u t could be conditionally homoskedastic, e.g. E ( u 2 t j X ) = & 2 and E ( u 2 t ) = & 2 & u t could be conditionally heteroskedastic, e.g. E ( u 2 t j X ) = & 2 x 2 t 1 and E ( u 2 t ) = & 2 E ( x 2 t 1 ) & u t could not be unconditionally heteroskedastic, e.g. E ( u 2 t j X ) = & & 2 x 2 t 1 for t < n & 2 x 2 t 2 for t ¡ n and E ( u 2 t ) = & & 2 E ( x 2 t 1 ) t < n &...
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Key Topics - Key Topics Probability Concepts Understand and...

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