205 Pages
English
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Applied Time Series Econometrics

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205 Pages
English

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This book attempts to demystify time series econometrics so as to equip macroeconomic researchers focusing on Africa with solid but accessible foundation in applied time series techniques that can deal with challenges of developing economic models using African data.

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Published 29 December 2012
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EAN13 9789966792396
Language English
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Exrait

. .
Geda Ndungʼu Zerfu
Applied Time Series Econometrics
This book attempts to demystify time series econometrics so as
to equip macroeconomic researchers focusing on Africa with
solid but accessible foundation in applied time series techniques A Practical Guide for Macroeconomic Researchers with a
that can deal with challenges of developing economic models
Focus on Africausing African data.
Alemayehu Geda is a Professor of Economics at the
Department of Economics, Faculty of Business and Economics, Addis
Ababa University, Ethiopia.
Njuguna Ndungʼu is currently the Governor of the Central Bank
of Kenya, he is an Associate Professor of Economics at the
University of Nairobi and holds a PhD in economics from the
University of Gothenburg, Sweden.
Alemayehu Geda
Daniel Zerfu is a Senior Research Economist at the Njuguna Ndung’u
Development Research Department, African Development
Daniel ZerfuBank. Before joining the Bank, he was an Assistant Professor of
Economics at the School of Economics, Addis Ababa University,
Ethiopia.
ISBN 978-9966-792-11-2
Roots of companion matrix1.00
0.75
4.3
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University of Nairobi Press AERC 9 789966 792112 UONP University of Nairobi Press






APPLIED TIME SERIES ECONOMETRICS
APPLIED TIME SERIES ECONOMETRICS
A Practical Guide for Macroeconomic Researchers
with a Focus on Africa
Alemayehu Geda
Njuguna Ndung’u
Daniel Zerfu
African Economic Research ConsortiumUniversity of Nairobi Press


First published 2012 by
University of Nairobi Press
Jomo Kenyatta Memorial Library
University of Nairobi
P.O. Box 30197 – 00100 Nairobi
© The University of Nairobi Press and African Economic Research Consortium
(AERC) 2012
The moral rights of the authors have been asserted.
The University of Nairobi Press supports and promotes the University’s objectives of
discovery, dissemination and preservation of knowledge, and stimulation of intellectual and
cultural life by publishing works of the highest quality in association with partners in
different parts of the world. In doing so, it adheres to the University’s tradition of
excellence, innovation and scholarship.
All rights reserved. Except for the quotation of fully acknowledged short passages for the
purposes of criticism, review, research or teaching, no part of this publication may be
reproduced, stored in any retrieval system, or transmitted in any form or means without
prior written permission from the University of Nairobi Press.
University of Nairobi Library CIP Data
Applied time-series econometrics: a practical guide for macroecomic researchers with a
focus on Africa / by A. Geda, N. Ndung’u and D. Zerfu. – Nairobi: University of
Nairobi Press, 2012.
205P.
ISBN–10–9966–792–11–2
ISBN–13–978–9966–792–11–2
1. Time-series analysis 2. Econometrics I. Geda, Alemyehu
II. Ndung’u, Njuguna III. Zerfu, Daniel
QA 280 .A66
Printed by:
Aliki Printers.
P.O. Box 9434 – 00300, Nairobi, Kenya
































Table of Contents

List of Figures ....................................................................................................................... vii
List of Tables ........................................................................................................................ viii
List of Illustrations .................................................................................................................. x
List of Boxes ............................................................................................................................ x
About Authors ....... xi
Preface and Acknowledgment .............................................................................................. xiii
Chapter 1
INTRODUCTION ................................................................................................................. 1
Chapter 2
MODEL SPECIFICATION ................................................................................................. 7
The Theoretical Model ............................................................................................................ 7
Data Exploration with STATA: A Brief View ........................................................................ 9
Narrowing Down the Research Question and Coping with Model Specification ................. 23
From Model Specification to Estimation .............................................................................. 25
Chapter 3
TIME SERIES PROPERTIES OF MACRO VARIABLES: TESTING FOR
UNIT ROOTS ...................................................................................................................... 27
Introduction........................................................................................................................... 27
Theoretical Time Series Issues .............................................................................................. 27
Unit Root Tests ..................................................................................................................... 35
Problems With Unit Root Testing ......................................................................................... 40
Chapter 4
COINTEGRATION ANALYSIS ....................................................................................... 45
Introduction to Cointegration (CI) and Error Correction Models (ECM) ............................. 45
The Engle-Granger (EG) Two-Step Approach ..................................................................... 45
Some Relevant Mathematical Concepts: Matrices and Eigen Values ................................... 55
Johansen’s Multivariate Approach: Identification of the Beta-coefficient and
Restriction Tests .................................................................................................................... 58
An Application of the Johansen Approach Using Ethiopian Consumption Data .................. 71























Modelling PPP using Data from Mozambique: The Nice Case of One Cointegration
Vector .................................................................................................................................... 80
Handling Two Cointegrating Vectors: Kenya’s Exchange Rate Model ................................ 85
Problems of Cointegration with I(2) Variables ................................................................... 109
Empirical Results: Capital Stock and Production Function for Ethiopia ............................ 112
Conclusion .......................................................................................................................... 115
Chapter 5
THE ECONOMETRICS OF FORECASTING: THEORY AND APPLICATION ... 117
Introduction......................................................................................................................... 117
Graphics for Forecasting.....................................................................................................118
The Box-Jenkins Approach to Forecasting ......................................................................... 135
Forecasting with Regression ............................................................................................... 136
Multiple Equation Forecasting Models ............................................................................... 138
Chapter 6
AN INTRODUCTION TO PANEL UNIT ROOTS AND COINTEGRATION ......... 145
Introduction...... 145
Panel Unit Root Tests ......................................................................................................... 146
Testing for Cointegration in Panel Data .............................................................................. 155
Illustration: Panel Cointegration Tests of an Oil Consumption Equation in
11 African Countries ........................................................................................................... 160
Conclusion .......................................................................................................................... 162
APPENDICES ................................................................................................................... 165
Appendix: Review of Basic Statistics for Time Series Econometrics ................................. 165
Reference and Further Readings ......................................................................................... 177
A GUIDE FOR FURTHER READINGS ........................................................................ 179
INDEX ................................................................................................................................ 187
vi









































































List of Figures
Figure 2.1: Scatter plot: Y1 on X1 ................................................................................... 122:ot: Y2 on X2 13
Figure 2.3: Scatter plot: Y3 on X3 133a:by removing the outlier ............................................ 14
Figure 2.4: Scatter plot: Y4 on X4 144a:by removing the outlier 15
Figure 2.5: Scatter plot of Ethiopian debt (1970–2001)................................................... 166:ot matrix of debt for some African countries (1970–2001) ............ 16
Figure 2.7: Box plots of debt for some African countries (1970–2001) .......................... 178: Changes in the distribution of wage income per month (1994–2000, by
quintile) ......................................................................................................... 18
Figure 2.9: Kernel density estimates of wage income (1994 and 2000) .......................... 1910: Functional forms that may fit Ghana’s pattern of debt (1970–2001) ............ 20
Figure 2.11: Box plots of Ethiopia’s debt and its logarithmic form (1970–2001) ............. 2112: Pattern of investment in Kenya: 1972–1999 ................................................. 22
Figure 2.13: Residuals and fitted values from STATA ...................................................... 2314: Normalised residuals and leverage from STATA ......................................... 23
Figure 3.1: Stationary and nonstationary time series variable 282: Covariance stationary and trend stationary variables .................................... 34
Figure 3.3: Nonstationary variable in levels and first difference ..................................... 344:variafirst difference 37
Figure 3.5: Actual and HP Filter of per capita agricultural output ................................... 416: Growth rate of agricultural output per capita ................................................ 42
Figure 3.7: Clement-Monta és-Reyes double IO test for unit root .................................. 43
Figure 4.1: Graphs of variables in levels and differences .............................................. 1122: Roots of companion matrix ......................................................................... 114
Figure 5.1: Kenya’s monthly exchange rate 1993–2000................................................ 1182: Mozambique price level: Monthly data for 1990–2001 .............................. 119
Figure 5.3: Growth in prices for Mozambique during 1990:12–2001:12 ...................... 1194: Actual and fitted trend values for LEX ....................................................... 121
Figure 5.5:nd fitted values with quadratic trend for LEX .............................. 1236: Forecast of LEX with evaluation statistics .................................................. 125
Figure 5.7: Forecasted values of the Kenyan exchange rate .......................................... 1268: MA (8) actual and fitted values ................................................................... 132
Figure 5.9: AR (3) actual and fitted values .................................................................... 13210: ARIMA (2, 1, 2) actual and fitted values .................................................... 132
Figure 5.11a: MA (8) forecast ........................................................................................... 13311b: ARIMA (2,1,2) ............................................................................................ 133