Econ 525: Time Series and Forecasting
Problem Set 1
Due on Feb 11, 2016
1. Suppose you toss a die. Let X denote the number of the side turning
up and the probability of each side turning up is as follows:.P (X = 1) =
P (X = 6) = 0:1, P (X = 2) = P (X = 5)

A few more words about R 2
Asymptotics for OLS with time series
Spurious regressions
Difference stationary vs. trend stationary
ECO 521
Lecture 9
Regression with Time Series Asymptotics
Denis Kwiatkowski
New York State Division of the Budget & Adjunct Lec

Financial Economics 466/566 - Due Tuesday April 12
Part A: Interest Rates, General Equilibrium, Comparative Statics (50 points)
This section builds on the general equilibrium model discussed in class. The purpose
of this assignment is to examine the compa

Introduction
Types of time series models
Finite sample properties of OLS
Binary and trending variables
ECO 521
Lecture 7
Regression with Time Series
Denis Kwiatkowski
New York State Division of the Budget & Adjunct Lecturer, University at Albany
March 1,

Weakly vs. strongly dependent data
ECO 521
Lecture 8
Regression with Time Series Weak Dependence
Denis Kwiatkowski
New York State Division of the Budget & Adjunct Lecturer, University at Albany
March 8, 2016
Denis Kwiatkowski
ECO 521 Lecture 8
Weakly vs.

Invertibility
Overdifferencing
ECO 521
Lecture 6
ARIMA Methods Continued
Denis Kwiatkowski
New York State Division of the Budget & Adjunct Lecturer, University at Albany
February 25, 2016
Denis Kwiatkowski
ECO 521 Lecture 6
Invertibility
Overdifferencing

AECO525 : Problem Set 2
Due on Mar 01, 2016
1. Consider the following AR(2) process:
yt
"t
=
0:7 + 0:2yt
W N (0; 1)
1
+ 0:1yt
2
+ "t :
(a) Is yt weakly stationary? Why?
(b) Compute E(yt ) and var(yt ):
(c) Derive the autocovariance function
1.
k for k
k
a

AECO525 : Answers to Problem Set 2
1. Write
yt = 0:7 + 0:2yt
1
+ 0:1yt
2
+ "t :
(a) Note that the AR(2) process can be rewritten as
yt
1 = 0:2(yt
1) + 0:1(yt
1
1) + "t
2
then
(1
0:1L2 )(yt
0:2L
1) = "t
Now need to solve
1
but
z
=
=
=
=
0:1z 2 = 0
0:2z
p
(

Econ 525: Time Series and Forecasting
Spring 2016
1. Note that
P (Xi
P (Xi
P (Xi
=
=
=
1) = P (Xi = 6) = 0:1
2) = P (Xi = 5) = 0:15
3) = P (Xi = 4) = 0:25
Hence
6
P
= EX =
Xi P (Xi )
i=1
= 0:1
= 3: 5
1 + 0:15
2 + 0:25
3 + 0:25
4 + 0:15
5 + 0:1
6
Next
EX 2

Practice Test 2
Show all work, clearly and in order, if you want to get full credit.
Circle or otherwise indicate your final answers.
1.
(20 points) True or False.
a. (5 pts) A random variable associates a numerical value with each outcome of a
chance e