# quiz_1 - , 2 ), compute the following quantities: (a)...

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AMS316 Quiz #1 1. Suppose that X 1 , . . ., X n are independent and identically distributed (i.i.d.) N ( μ, σ 2 ) ( σ 2 is known). (a) What is the maximum likelihood estimate of μ ? (b) What is the distribution of your estimate? 2. Consider the process x t = a + bt + s t + y t , in which s t is a deterministic process satisfying s t = s t - 12 and s t + · · · + s t +11 = 0, y t is a stationary process with mean zero. (a) What are the trend and seasonal components in the process x t ? (b) Is the process z t stationary? 3. Let { x t } be a process given by x t = z t + θz t - 2 , where z t i.i.d. Normal(0
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Unformatted text preview: , 2 ), compute the following quantities: (a) Autocovariance functions ( k ) for k 0. (b) Autocorrelation functions ( k ) for k 0. 4. Consider the AR(1) process (-1 &amp;lt; &amp;lt; 1): x t = x t-1 + t , in which t are independent and identically distributed (i.i.d.) normal random variables with mean 0 and variance 2 . Show that the autocorrelation of this process is ( k ) = k , for any integer k &amp;gt; 0....
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## This note was uploaded on 08/08/2010 for the course AMS 316 taught by Professor Xing during the Fall '09 term at SUNY Stony Brook.

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