African School of Economics
MMES - Econometrics
Practice Exercises for Final Exam
Exercise 1
Find whether the following AR models are stationary or not. If the model is stationary,
t ;Yt+h )
nd E (yt ) ; V ar (yt ) ; h = Cov (Yt ; Yt+h ) and h = Cov(Y
, f

African School of Economics
MMES - Econometrics
Midterm Practice: Solution
QuestionP1
a) x = N1 N
xi is the observed proportion of "wins."
i=1
1 PN
b) pb = x = N i=1 xi = 0:45 is the estimated probability of winning.
c) V ar (b
p) = p(1100p) , which is es

African School of Economics
Spring Semester
MMES - Econometrics
Instructor: Rachidi Kotchoni
Home Assignment#2: Solution
Question 1
Use the enclosed matlab code to Homework2_1.m to answer question 1. Here is an
example of output:
Y
2:0018
0:0018
0:0890
0:

African School of Economics
Spring Semester
MMES - Econometrics
Instructor: Rachidi Kotchoni
Home Assignment#1
Today: 2015-01-26
Due: 2015-02-12
Note: May be done in groups of 3 or 4 students.
Exercice 1 (6 points/20)
Consider the following linear model:

African School of Economics
MMES - Econometrics
Midterm Practice
Question 1
A money machine works as follows: you insert one dollar and press a button; the machine
may return two dollars (meaning that you win), or nothing (meaning that you loose). You dec

African School of Economics
MMES - Econometrics II
Instructor: Rachidi Kotchoni
Home Assignment #1
Today: March 1st, 2016
Due: March 31st, 2016
Note: May be done in groups of 2 or 3 students. Use your preferred software to answer the questions.
Your submi

African School of Economics
MMES - Econometrics II
Instructor: Rachidi Kotchoni
Home Assignment#2
Today: March 8, 2016
Due: April 8, 2016
Note: May be done in groups of 2 or 3 students.
Question 1 (8 points)
Consider the MA(1) model given by:
y t = c + "t

Violation of the Classical Assumptions in Linear
Regression Models
Rachidi Kotchoni
African School of Economics
January 11, 2016
R. Kotchoni (African School of Economics)
Violation of the Classical Assumptions
January 11, 2016
1 / 32
The Linear Regression

Maximum Likelihood Estimation
Rachidi Kotchoni
A.S.E.
January 11, 2016
R. Kotchoni (A.S.E. )
Maximum Likelihood
January 11, 2016
1 / 32
Principle of Maximum Likelihood
Consider a random variable Y
N , 2
The density of Y is given by:
1
f (y ) = p
exp
2
(y

Generalized Method of Moment
Rachidi Kotchoni
A.S.E.
Jan-May 2015
R. Kotchoni (A.S.E. )
Generalized Method of Moment
Jan-May 2015
1 / 32
Principle of Asset Pricing
Consider an asset that promises non-random cash ows dt ,
t = 1, 2, ., .
Suppose the interes

Review of Bivariate Analysis
Rachidi Kotchoni
African School of Economics
January 11, 2016
R. Kotchoni (A.S.E)
Bivariate Analysis
January 11, 2016
1 / 30
1. Joint distributions
Discrete Case
Consider rolling two dices, labelled "die 1" and "die 2".
Let X

Time Series Analysis
Basic Concepts
Rachidi Kotchoni
A.S.E
January 11, 2016
R. Kotchoni (A.S.E )
Time Series Analysis
January 11, 2016
1 / 47
Types of Time Series
A time series is a variable that describes a statistical entity over time.
The value taken b

Markov Switching and Conditional Mixture Models
Rachidi Kotchoni
A.S.E.
Jan-May 2015
R. Kotchoni (A.S.E. )
Markov Switching and Mixture
Jan-May 2015
1 / 31
Markov Chain
labels
Consider a discrete univariate Markov process st with possible values
1, 2, .,

Limited Dependent Variables
Rachidi Kotchoni
African School of Economics
January 11, 2016
R. Kotchoni (African School of Economics)
Limited Dependent Variables
January 11, 2016
1 / 22
Limited dependent variables
Denition
A limited variable is a variable w