Math 4506
Spring 2015
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
Take-home Final Exam
Spring 2014
NAME:
Instructions. This exam is due 48 hours after the time at which you requested to receive
it. If you return the exam late, you will lose 10 points for every hour (o
Brooklyn College
Department of Mathematics
Midterm Exam Solutions
Math 4506
Spring 2015
1. T, T, F, T, T, F, T
2. 2, 8, 4, 3
3. (a) We can re-write the dening equation as
(B)Xt = (B)Zt ,
1
where (B) = 1 + 2 B and (B) = 1 + 1 B + 1 B 2 . Now
2
2
1
(z) = 1
Brooklyn College
Department of Mathematics
Take-home Final Exam Solutions
Math 4506
Spring 2014
1. F, T, F, F, F
2. The Box-Pierce statistic is
k
approx
(i)2 2 ,
k
Q=n
i=1
where k should be taken to be at most log10 n. In this particular problem, since n
Brooklyn College
Department of Mathematics
Course Information
Math 4506
Spring 2015
Room and Schedule: 330 NE; Monday, Wednesday, 3:40 p.m. - 5:20 p.m.
Text: Time Series Analysis: With Applications in R (2nd Edition), by Jonathan D. Cryer and Kung-Sik Cha
Math 4506
Spring 2015
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
Brooklyn College
Department of Mathematics
Take-home Final Exam
Spring 2013
NAME:
Instructions. This exam is due at the time indicated in the e-mail in which you were sent
the exam (this time is based on your request). If you return the exam lat
Math 4506
Spring 2015
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 2015
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 Problems 1 and
2, make
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
Brooklyn College, CUNY
Math 4506 Time Series
Lecture Notes
Spring 2015
Christian Bene
s
cbenes@brooklyn.cuny.edu
http:/userhome.brooklyn.cuny.edu/cbenes/timeseries.html
Math 4506 (Spring 2015)
Prof. Christian Bene
s
January 28, 2015
Lecture #1: Introducti
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
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.
(