# hw1 - ∇ x t = x t ± x t-1 is stationary by ﬁnding its...

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- The homework has to be stapled. PSTAT 174/274. Homework #1 Name: Due: 10/16/06 at the beginning of the discussion session Score: /10 Credit: People you worked with: Sources consulted(Reference): 1. (2 points each) Consider the time series x t = β 1 + β 2 t + w t , where β 1 and β 2 are known constants and w t is a white noise process with variance σ 2 . (a) Determine whether x t is stationary. If x t is not stationary, exhibit a transformation that produces a stationary process. (b) Show that the mean of the moving average y t = 1 1 + 2 q q X j = - q x t - j is β 1 + β 2 t and give a simpliﬁed expression for the autocovariance function. (c) Prove that the ﬁrst diﬀerence series
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Unformatted text preview: ∇ x t = x t ± x t-1 is stationary by ﬁnding its mean and autocovariance function. 2. (2 points each) For a moving average process of the form x t = w t-1 + 2 w t + w t +1 where w t are independent with zero means and variance σ 2 w , determine the autocovariance and autocorrelation function of lag h = s ± t and plot. 3. (2 points) Consider the series x t = sin(2 πut ) , t = 1 , 2 , ··· , where u has a uniform probability distribution on the interval (0,1) Prove x t is weakly stationary....
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## This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.

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