Christiano
FINC 520, Spring 2007
Midterm Exam.
Here are some trigonometric properties that you may nd useful:
sin (k ) = 0, integer k, sin (/2) = 1
cos (0) = 1, cos (/2) = 0, cos () = 1
exp (i ) = cos () + i sin () .
There are 100 points possible on this
Christiano
FINC 520, Spring 2007
Final Exam.
Please do this exam on your own. It is due in Emiliano Pagnottas box
by noon, Thursday.
1. Consider the time series model you estimated in question 3, part (d) of
homework #7. Do a bootstrap on the ARCH(2) mode
Christiano
FINC 520, Spring 2008
Midterm Exam.
There are 100 points possible on this exam. The number of points allocated to each question are indicated, so you can allocate your time accordingly.
1. (12) Consider the stochastic process,
i
yt = i + i , i
Christiano
FINC 520, Spring 2008
Final Exam.
This is a closed book exam. Points associated with each question are
provided in parentheses. Good luck!
1. (20) Consider a stochastic process, at , which is the sum of two stochastic
processes, aT , and aP , w
Christiano
FINC 520 Midterm
Spring 2009
1. Suppose yt is an ARMA(p,q) process, i.e.
yt =
1 yt 1
+
where E ["2 ] =
t
2 yt 2
2
":
+ : +
p yt p
t ; F;
1 "t 1
+
2 "t 2
+ : +
q "t q ;
Write the ARMA(p,q) process in an VAR(1) process
t
Write down
+ "t +
vt ; an
Christiano
FINC 520, Spring 2008
Final Exam.
This is a closed book exam. Points associated with each question are
provided in parentheses. Good luck!
1. Prove the law of iterated mathematical expectations:
Ex = E [Exjy ] ;
where x and y are two random var
Christiano
FINC 520, Spring 2010
Midterm Exam.
There are 100 points possible on this exam. The number of points allocated to each question are indicated, so you can allocate your time accordingly. The density function for a normal random variable, x; is:
Christiano
FINC 520, Spring 2010
Homework 8, due May 30.
1. This question studies the Monte Carlo Markov Chain (MCMC) algorithm and the Laplace approximation. Because we do this in an example where we know the true distribution being approximated, we have
FINC-520
Christiano
Wold Representation Theorem
We have discussed a class of ARMA models and derived restrictions which ensure they
are models for covariance stationary time series. We have shown that these ARMA models
imply the data are a linear combinat
Christiano
FINC 520, Spring 2009
Homework 1, due Wednesday, April 8.
1. Consider a stochastic process with covariance function, 0 > 0, |1 | <
1
, j = 0, j 2. Identify two MA(1) representations for xt :
20
2
xt = t + t1 , t white noise with variance .
2
T
Christiano
FINC 520, Spring 2009
Homework 8, due Thursday, June 4.
1. Consider the iid Normal stochastic process, cfw_xt , with Ext = and
E (xt )2 = 2 . Let l = E (xt )l denote the lth moment about
the mean. A property of the Normal distribution is that
Christiano
FINC 520, Spring 2009
Homework 7, due Thursday, May 28.
1. We describe a model economy in terms of its equilibrium conditions,
expressed in linearized form:
Et t+1 + xt t = 0 (1)
[rt Et t+1 rrt ] + Et xt+1 xt = 0 (2)
ut + t + x xt rt = 0 (3)
r