gretl: http:/gretl.sourceforge.net/
Gnu Regression, Econometrics and Time-series Library
Gretl is a cross-platform software package for econometric analysis, written in
the C programming language. It is is free, open-source software. You may
redistribute
Using gretl for Principles of Econometrics, 3rd Edition
Version 1.3131
Lee C. Adkins
Professor of Economics
Oklahoma State University
May 8, 2010
1
Visit http:/www.LearnEconometrics.com/gretl.html for the latest version of this book. Also, check
the errat
TIME-SERIES ANALYSIS: PASCAL PROGRAM
This program demonstrates alternative ways of characterising a stationary
stochastic process. On the one hand are the time-domain characterisations,
which depend upon the autocorrelation and partial autocorrelation fun
EXERCISE: Fitting Trend Functions to Nonstationary Data
In order to understand the methods for estimating trend functions that are available in
the IDEOLOG program, you are invited to follow the instructions that are given in the
les CONSLOG, SALESLOG, HE
D.S.G. POLLOCK: TOPICS IN ECONOMETRICS 2011
1. EXPECTATIONS AND CONDITIONAL EXPECTATIONS
The joint density function of x and y is
f (x, y ) = f (x|y )f (y ) = f (y |x)f (x),
(1)
where
f (x, y )dx
f (x) =
and
f (y ) =
f (x, y )dy
y
(2)
x
are the marginal d
By following the sequence of commands recorded in this log, you will be able to fit a trend to the
monthly data on U.S. Retail Sales. Using one of the facilities of the program, you will also be
able to extract the seasonal component from the data.
.
IDEO
LECTURE 1
1. Let y = E (y |x) be the conditional expectation of y given x. Prove that
E cfw_(y y )2 E cfw_(y )2 , where = (x) is any other function of x.
Show that E x(y y ) = 0 and give an interpretation of this condition.
Demonstrate that, if E (y |x)
EXERCISE: Analysis of the Pearson Height Data using GRETL
The Pearson data on the height of fathers v 1 and the height of sons v 2 is in
a plain text (ASCII) le labelled Pearson.txt. These can be brought in gretl
using using the hFile i hOpen Data i hImpo
EXERCISE: Analysis of Panel Data using GRETL
The Data From Greene. The gretl program is already linked to a data
le greene14 1.gdt, which is designed to illustrate the analysis of panel data.
The data le can be loaded via the menu commands hFile ihOpen Da
By following the sequence of commands recorded in this log, you will be able to extract a trendcycle component from the monthly data on U.S. Retail Sales. The end effects are controlled by
inserting an extrapolation between the end and the beginning of th
ASTSA :http:/www.stat.pitt.edu/stoffer/tsa2/
ASTSA is a Windows time series package that is distributed as Freeware
and is provided As is without warranty of any kind, either expressed or implied.
ASTSA may not be distributed as a component of any commerc
A GUIDE TO MESOSAUR: A PROGRAM FOR THE
STATISTICAL ANALYSIS OF TIME SERIES
MESOSAUR is a computer program for the statistical analysis of time series,
which was created by a team of programmers and statisticians at the Central
Economics and Mathematics In
ECONOMETRIC THEORY: Exercise 1 (Tutorial)
Matrix Algebra and Manpower Planning
Matrix Multiplication in Microsoft Excel
There is a limited set of matrix operations which may be performed in Excel
with the use of predened commands. The following commands a
EXERCISE: Models with Limited Dependent Variables
A Logistic Model of the Decision to Smoke or not to Smoke
Within the document Smoking and Drinking Amongst Adults 2008, which is
a component of the General Lifestyle Survey 2008, you will nd Table 1.3
Perc
FILTERING MACROECONOMIC DATA
WienerKolmogorov Filtering of Stationary Sequences
The classical theory of linear ltering was formulated independently by
Norbert Wiener (1941) and Andrei Nikolaevich Kolmogorov (1941) during
the Second World War. They were bo
EC3062 ECONOMETRICS
DYNAMIC REGRESSIONS MODELS
Autoregressive Disturbance Processes
Economic variables often follow slowly-evolving trends and they tend to be
strongly correlated with each other. If the disturbance term is compounded
from such variables,
EC3062 ECONOMETRICS
LIMITED DEPENDENT VARIABLES
Logistic Trends
One way of modelling a process of bounded growth is via a logistic
function. See Figure 1. This has been used to model the growth of a
population of animals in an environment with limited foo
EC3062 ECONOMETRICS
MATRIX KRONECKER PRODUCTS
Consider the matrix equation Y = AXB . When all of the factors are 2 2
matrices, this becomes
y11
y21
y12
y22
=
a11
a21
a12
a22
x11
x21
x12
x22
x
x11
, A 12
x21
x22
=
A
=
b11 A
b11
b12
b11
b12
b21
b22
b21
b22
EC3062 ECONOMETRICS
HYPOTHESIS TESTS FOR THE CLASSICAL LINEAR MODEL
The Normal Distribution and the Sampling Distributions
To denote that x is a normally distributed random variable with a mean
of E (x) = and a dispersion matrix of D(x) = , we shall write
EC3062 ECONOMETRICS
IDENTIFICATION OF ARMA MODELS
A stationary stochastic process can be characterised, equivalently, by its
autocovariance function or its partial autocovariance function.
It can also be characterised by is spectral density function, whic
EC3062 ECONOMETRICS
LINEAR STOCHASTIC MODELS
Let cfw_x +1 , x +2 , . . . , x +n denote n consecutive elements from a stochastic process. If their joint distribution does not depend on , regardless of
the size of n, then the process is strictly stationary
EC3062 ECONOMETRICS
THE MULTIPLE REGRESSION MODEL
Consider T realisations of the regression equation
y = 0 + 1 x1 + + k xk + ,
(1)
which can be written in the following form:
y1
1
y2 1
. =.
. .
.
.
1
yT
(2)
x11
x21
.
.
.
xT 1
0
x1k
1
x2k 1 2
. . + .
EC3062 ECONOMETRICS
ELEMENTARY REGRESSION ANALYSIS
We shall consider three methods for estimating statistical parameters.
These are the method of moments, the method of least squares and the
principle of maximum likelihood.
In the case of the regression m
IDEOLOG: A PROGRAM FOR FILTERING
ECONOMETRIC DATAA SYNOPSIS
OF ALTERNATIVE METHODS
By D.S.G. POLLOCK
University of Leicester
Email: stephen [email protected]
An account is given of various ltering procedures that have been implemented in a
compute
EXERCISE: Testing an Hypothesis
Regarding Pearsons Data on Heights
From the evidence of Figure 1 of Lecture 1, which shows two regression lines tted
to Pearsons data, there seems to have been a signicant increase in the heights of
adult males from one gen
By following the sequence of commands recorded in this log, you will be able to fit a flexible
trend function to the logarithms of 129 annual observations on U.K. GDP. The flexible trend will
accommodate the structural breaks that followed two world wars.
Gretl Users Guide
Gnu Regression, Econometrics and Time-series
Allin Cottrell
Department of Economics
Wake Forest university
Riccardo Jack Lucchetti
Dipartimento di Economia
Universit Politecnica delle Marche
December, 2008
Permission is granted to copy,
ECONOMETRIC THEORY: Exercise 2
Matrix Multiplication: Orthonormal Matrices and Rotations.
1. Find following matrix product:
S1
0
1
1
0
S2
S1
0
0
.
S2
2. Conrm that, if = 45 , then
cos
sin
sin
cos
1
2
1
2
=
1
2
1
2
.
3. Use the denitions of a sine and
EXERCISE: Estimating the Relationship Between
Aggregate Income and Consumption
The purpose of this exercise is to show how one might model the relationship
between two trended variables. The variables of the example are the quarterly
data on aggregate con
By following the sequence of commands recorded in this log, you will be able to extract a trendcycle component from the data on U.K. Consumption. There are three alternative pathways to
the same end result, which are TRACKS A, B and C. The diversions occu