Texts: QUESTION TWO
A time series of n=100 observations gave the following sample ACF and sample PACF:
Lag k 1 2 3 4 5 6 7 8
TK 0.22 -0.68 -0.47 -0.34 0.56 100- -0.51 -0.26
PKK 0.22 -0.76 0.09 0.05 0.09 0.04 -0.11 110-
with the sample mean Z=10.04 and sample variance σ^2=2.77. An AR(2) model, 1-B-BZ=ϵ+a, appears to be appropriate for the data.
i. Obtain the Yule-Walker estimates.
ii. Using α and β as the true values of α and β, calculate PKK for k=1, 2, 3. [4 marks] [4 marks]
b. Consider the following set of data:
{23.32, 32.33, 32.88, 28.98, 33.16, 26.33, 29.88}
Calculate the lag-two sample autocorrelation of the time series. [3 marks]
c. Consider the MA(1) process Y_t = ε_t + ε_t-1, where ε ~ N(0, σ^2).
Show that the correlation [4 marks].
