Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam
Spring 2014
Instructions. You are allowed to use a two-sided 8.5 11 set of notes. You must show
all your work and cross out any work you do not want graded. Except on Problem 1, make
sure y
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam Solutions
Spring 2011
1. (a) False; the two things have nothing to do with each other. The time series cfw_Xt
dened by Xt = N (t, 1) is Gaussian (since each random variable is normal), but
Brooklyn College
Department of Mathematics
Midterm Exam - Partial Solutions
Math 4506
Spring 2014
1. T, T, T, T, T, T, F, F, F
2. The easiest way to solve this problem is to note that Yt is in fact the AR(1) process
1
Yt = Yt1 + Zt
4
in its causal form.
(
Math 4506
Spring 2014
Homework 1 Solutions
Note: In some cases where the solution is straightforward, I may just write what the main idea
is to solve the problem. If you wish to know more, come and see me so we can talk about it.
1. This is nothing more t
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam
Spring 2013
Instructions. You are allowed to use one 2-sided 8.5 11 sheet of notes, a calculator,
and a pen or pencil, but nothing else. In particular, if at any point of the exam you use
a
Math 4506
Spring 2014
Homework 2 Solutions
1. Textbook Problem 2.7: Since cfw_Yt is stationary, E[Yt ] = Y for all t and cfw_Yt has an autocovariance function Y . Therefore,
(a)
E[Wt ] = E[Yt Yt1 ] = E[Yt ] E[Yt1 ] = Y Y = 0.
Cov(Wt , Wt+h ) =
=
=
=
(1)
Math 4506
Spring 2014
Homework 3 Solutions
1. (a) The ACF of an MA(1) process has a non-zero value only at lags 1, 0, and 1. Problem
4.3 from the textbook (which you didnt do, so I didnt expect you to mention this)
shows that |(1)| 1 .
2
(b) The ACF of an
Math 4506
Brooklyn College
Department of Mathematics
Midterm Exam
Spring 2011
Instructions. You are allowed to use a one-sided 8.5 11 set of notes. You must show
all your work and cross out any work you do not want graded. Except on Problems 1 and
2, make