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Homework 2
STAT 443
Spring 2007
1. (20 points) Let {Zt} be a sequence of independent normal random
variables with zero mean (E(Zt)=0) and common finite variance
(Var(Zt)=s^2). For each process below define the mean and autocovariance
function. Which, if any, of the following processes are (weakly)
stationary? Justify your answer.
a) Xt =a + bZt1 + cZt2 for some constants a, b and c;
b) Xt= 2Zt sin(t)cos(t).
2.
(30 points)
DESCRIPTIVE ABSTRACT:
The dataset consumpt.txt contains yearly data on 3 month Treasury bill
rate (TBILL) in US dollars and per capita real consumption (CONS) in
USA from 1964 to 1995.
VARIABLE DESCRIPTIONS:
YEAR  from 1964 to 1995 (the training set is from 1964 to 1992)
CONS – per capita real consumption
TBILL – 3 month Treasure bill rate
RSERV  services, in billion dollars of 1992.
Values are aligned and delimited by blanks.
YOUR TASK:
To forecast per capita consumption for 1993, 1994 and 1995 using the 3
month Treasury Bills rates. The training window is from 19641992. You
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This note was uploaded on 01/12/2012 for the course STAT 443 taught by Professor Yuliagel during the Spring '09 term at Waterloo.
 Spring '09
 YuliaGel
 Covariance, Forecasting, Variance

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