IDS 476
Assignment #2 - Sample Covariance and Correlation; Simulation of Short Series
Use Excel (or pencil, paper, and calculator). Due on Tuesday, 5-Sept-2006.
1. Sample Covariance and Correlation. The following are temperature measurements
made every minute on a chemical reactor:
200, 202, 208, 204, 204, 207, 207, 204, 202, 199
(1) Calculate C0, C1, C2, C3, r1, r2 and r3 for the series given above. Make a graph of
rk, k = 0, 1, 2, 3, in the manner of Fig. 2.4, p. 2.14.
(2) Compute approximate standard errors for rk, k = 1, 2, 3, that is, SE(r1), SE(r2),
SE(r3), using the displayed formulas for these on p. 2.7.
2. Simulation of Series. The following table gives a set of random shocks
a0, a1, . . . , a10.
t | 0 1 2 3 4 5 6 7 8 9 10
at | -0.3 0.6 0.9 0.2 0.1 -0.6 1.7 -0.9 -1.3 -0.6 -0.4
Now consider the models:
(a) Yt = 0.2 Yt-1 + at
(b) Yt = et , where et = at – 0.5 at-1
(c) Yt = 0.8 Yt-1 + et , where et = at – 0.5 at-1
(i) Use the above models to obtain Y1, Y2, …, Y10, for each of the models
(assuming that Y0 = Y-1 = Y-2 = 0 if necessary)
(ii) Plot the generated series in each case.
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Created 2004: August 23 Latest revision 2006: Feb 11
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