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# hwk5soln - 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 Assignment #5 Suggested Solutions Out of 24 possible points Note: BJR refers to class text: Time Series Analysis: Forecasting and Control, 4th Edition by Box, Jenkins, Reinsel (2008). 1.a (2 pts) Figure 1: Plots of CRSP Decile 1 portfolio return. There seems to be some short-term dependence here based on the ACF and the PACF plots. 1

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1.b (2 pts) z t = 0 . 015 + (1 + 0 . 216 B ) a t , ˆ σ 2 a = 0 . 0035 1.c (3 pts) Steps Ahead 1 2 3 4 MA(1) Pred 0.0126 0.0146 0.0146 0.0146 SE Pred 0.059 0.0604 0.0604 0.0604 A ﬁnite order MA has mean reverting predictions, since it has limited memory. A MA(1) model will simply predict the unconditional mean from 2 steps forward. 1.d (2 pts) (1 - 0 . 20 B )( z t - 0 . 015) = a t , a t N (0 , 0 . 0035) 1.e (2 pts) Steps Ahead 1 2 3 4 AR(1) Pred 0.0112 0.0139 0.0144 0.0145 SE Pred 0.0591 0.0603 0.0603 0.0603 2
1.f (3 pts) Figure 2: Prediction Plot from MA(1) and AR(1) models.

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hwk5soln - STSCI 4550 ILRST 4550 ORIE 5550 Applied Time...

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