exam1soln - STSCI 4550 ILRST 4550 ORIE 5550 Applied Time...

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STSCI 4550 / ILRST 4550 / ORIE 5550 Applied Time Series Analysis, Spring 2012 Professor David S. Matteson Exam #1 Suggested Solutions Out of 100 possible points 1. The figure above contains plots of six different time series. (i) Which of the series (a)-(f) appear non-stationary? [5] a,c,f (ii) For each of the series which appear non-stationary, briefly state why. [5] a - random walk c - appears cyclic f - increasing variance (iii) For each of the series which appear non-stationary, is there a simple transformation that would lead to a stationary series? If so, state it. [5] a - first order differencing 1-B c - apply backshift operator (seasonal) f - rescale relative to the time index y t = x t /t α , where α is something like 0.5, 1, or 2. 2. The figure above contains plots of four different time series. Match each of the series (a)-(d) with one of the following processes: [10] (i) White noise d (ii) AR(1) c (iii) MA(1) a (iv) Random walk b 3. The figure above contains plots of the sample auto-correlation functions (ACF) for four different time series. Match each of the ACF(s) (a)-(d) with one of the following processes: [10] (i) White noise a (ii) AR(1) c (iii) MA(1) d 1
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(iv) Random walk b 4. Let a t be a stationary Gaussian process.
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