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hwk3soln - 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 #3 Suggested Solutions Out of 23 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) Lag 1 2 3 4 5 6 7 8 9 10 11 12 ACF 0.20 -0.05 -0.13 -0.09 -0.08 -0.03 -0.07 -0.02 -0.08 0.03 0.12 0.14 PACF 0.20 -0.10 -0.10 -0.05 -0.07 -0.02 -0.09 -0.02 -0.10 0.03 0.08 0.08 Lag 13 14 15 16 17 18 19 20 21 22 23 24 ACF -0.02 -0.09 -0.12 -0.05 -0.09 -0.10 -0.03 0.05 -0.00 0.01 0.09 0.15 PACF -0.07 -0.06 -0.07 -0.02 -0.11 -0.10 -0.02 0.02 -0.06 -0.05 0.05 0.09 1.b (2 pts) H 0 : ρ 1 = ρ 2 = ... = ρ 12 = 0 H A : At least one ρ i 6 = 0 , i ∈ { 1 , ..., 12 } By the Box-Ljung test, we have a χ 2 test statistic of 30.01 on a Null χ 2 12 distribution, resulting in a p-value of 0 . 003 < 0 . 05. We can thus reject H 0 at the 5% level to conclude that the first 12 lags of ACF are not all zero. 1.c (2 pts) H 0 : ρ 12 = 0 H A : ρ 12 6 = 0 ˆ ρ 12 = 0 . 145, while under H 0 , SE ρ 12 ) 1 n = 1 228 . This results in a t-statistic of 2 . 189 on a Null t df =227 distribution, which gives a p-value of 0 . 015 < 0 . 05, so we can reject H 0 at the 5% level to conclude that ρ 12 6 = 0.
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