EX.4 Time series
1. Verify that the autoregressive process
Xt = (Xt-1 + Xt-2)/12 +Zt
where cfw_Zt is white noise , is stationary, and find its autocorrelation function.
2. Plot the autocorrelation function (up to lag 10) of the second order autoregressive

Exercise 3
1. The following is the yearly coee production (in coded units) of a certain country from 1991
to 2000.
Year
Coee production
91
92
13.0 14.0
93
94
15.0 11.8
95
96
16.5 18.1
97
12.0
98
99
15.0 13.0
00
17.0
(a) Calculate the forecast for 1996 to

Time Series Ex.2
1. It was determined that a quadratic model was thc best fit of thc trend for 12 years
of data. The data are
22, 18, 21, 19, 17, 16 ,18 ,21, 20, 23, 22, 25
The results from running a multiple regression on these data arc as follows:
corr(

Ex.5 Time series
1. Find the partial ACF of the AR(2) process given by
Xt=(1/3)Xt-1+ (2/9)Xt-2 + at
2. Sketch the autocorrelation function of the process
yt=-0.5yt-1+at-0.8at-1
3. Is the model
yt = -0.2yt-1+0.48yt-2+ at+0.6at-1-0.16at-2
over-parametrised?