time series analysis of saudi arabia oil production data a thesis submitted to the graduate school in

135 Pages·2013·13.36 MB·English

TIME SERIES ANALYSIS OF SAUDI ARABIA OIL
PRODUCTION DATA
A THESIS
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS
FOR THE DEGREE
MASTER OF SCIENCE
BY
ABDULMAJEED ALBARRAK
ADVISER DR. RAHMATULLAH IMON
BALL STATE UNIVERSITY
MUNCIE, INDIANA
DECEMBER, 2013
Time Series Analysis of Saudi Arabia Oil Production Data
A THESIS
SUBMITTED TO THE GRADUATE EDUCATIONAL POLLCIES COUNCIL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
MASTER OF SCIENCE
By
Abdulmajeed Albarrak
Committee Approval:
………………………………………………………………………………………………….
Committee Chairman Date
………………………………………………………………………………………………
Committee Member Date
…………………………………………………………………………………………………
Committee Member Date
Department Head Approval:
…………………………………………………………………………………………………
Head of Department Date
Graduate office Check:
…………………………………………………………………………………………………
Dean of Graduate School
Date
Ball State University
Muncie, Indiana
November 2013
ACKNOWLEDGEMENTS

Foremost, I would like to express my sincere gratitude to my advisor Professor Dr. Rahmatullah
Imon for the continuous support of my thesis study, for his patience, motivation, enthusiasm, and
immense knowledge. His guidance helped me in all the time during my analysis and writing the
report. I could not have imagined having a better advisor and mentor for my thesis other than
him. Besides my advisor, I would like to thank the rest of my thesis committee: Dr. Dale
Umbach and Dr. Munni Begum for their encouragement, insightful comments and patience. I am
thankful to all my classmates for their kind supports. Last but not the least, I would like to thank
my family: my parents, my brothers and sisters, for supporting me throughout my life.

Abdulmajeed Albarrak
November 3, 2013
ABSTRACT
THESIS PAPER: Time series analysis of Saudi Arabia oil production data
STUDENT: Abdulmajeed Albarrak
DEGREE: Master of Science
COLLEGE: Sciences and Humanities
DATE: December, 2013
PAGES: 123
Saudi Arabia is the largest petroleum producer and exporter in the world. Saudi Arabian
economy hugely depends on production and export of oil. This motivates us to do research on oil
production of Saudi Arabia. In our research the prime objective is to find the most appropriate
models for analyzing Saudi Arabia oil production data. Initially we think of considering
integrated autoregressive moving average (ARIMA) models to fit the data. But most of the
variables under study show some kind of volatility and for this reason we finally decide to
consider autoregressive conditional heteroscedastic (ARCH) models for them. If there is no
ARCH effect, it will automatically become an ARIMA model. But the existence of missing
values for almost each of the variable makes the analysis part complicated since the estimation of
parameters in an ARCH model does not converge when observations are missing. As a remedy
to this problem we estimate missing observations first. We employ the expectation maximization
(EM) algorithm for estimating the missing values. But since our data are time series data, any
simple EM algorithm is not appropriate for them. There is also evidence of the presence of
outliers in the data. Therefore we finally employ robust regression least trimmed squares (LTS)
based EM algorithm to estimate the missing values. After the estimation of missing values we
employ the White test to select the most appropriate ARCH models for all sixteen variables
under study. Normality test on resulting residuals is performed for each of the variable to check
the validity of the fitted model.
Table of Contents
CHAPTER 1 1
INTRODUCTION
  1

1.1 The History of Oil Production in Saudi Arabia 1
1.2 Saudi Arabia Oil Production Data 3
1.3 Outline of the Study 13
CHAPTER 2 15
ARCH/GARCH
 MODELS,
 OUTLIERS
 AND
 ROBUSTNESS,
 TESTS
 FOR
 NORMALITY
 AND
 ESTIMATION

OF
 MISSING
 VALUES
 IN
 TIME
 SERIES
  15

2.1 ARCH and GARCH Models 15
2.2 Outliers and Robustness 28
2.3 Tests for Normality 35
2.4 Estimation of Missing values 37
2.5 Computation 41
CHAPTER 3 42
OUTLIER
 ANALYSIS
 AND
 ESTIMATION
 OF
 MISSING
 VALUES
 BY
 ROBUST
 EM
 ALGORITHM
 FOR

SAUDI
 ARABIA
 OIL
 PRODUCTION
 DATA
  42

3.1 Outlier Analysis 42
3.2 Estimation of Missing Values 45
CHAPTER 4 61
SELECTION
 OF
 ARCH
 MODELS
 FOR
 SAUDI
 ARABIA
 OIL
 PRODUCTION
 DATA
  61

4.1 Crude Oil Production 61
4.2 Total Export of Refined Oil 67
4.3 Export of Crude Oil to North America 70
4.4 Export of Refined Oil to North America 73
4.5 Export of Crude Oil to South America 76
4.6 Export of Refined Oil to South America 79
4.7 Export of Crude Oil to Western Europe 82
4.9 Export of Crude Oil to Middle East 88
4.10 Export of Refined Oil to Middle East 90
4.11 Export of Crude Oil to Africa 93
4.12 Export of Refined Oil to Africa 96
4.13 Export of Crude Oil to Asia and Far East 99
4.14 Export of Refined Oil to Asia and Far East 103
4.15 Export of Crude Oil to Oceania 106
4.16 Export of Refined Oil to Oceania 108
4.17 Result Summary 111
CHAPTER 5 113
CONCLUSIONS
 AND
 DIRECTION
 OF
  113

FUTURE
 RESEARCH
  113

5.1 Conclusions 113
5.2 Direction of Future Research 114
REFERENCES 115
APPENDIX 117
List of Tables
CHAPTER 2
Table 2.1: Specification of ARCH Models 27
CHAPTER 3
Table 3.1 Estimates of Missing Values for the Saudi Arabia Oil Production Data 46
CHAPTER 4
Table 4.1.1 The ACF and PACF Values for the Crude Oil Production Data 61
Table 4.1.2 Order of ARCH Using the White Test for the Crude Oil Production Data 63
Table 4.1.3 Order of ARCH Using the Breusch-Pagan Test for the Crude Oil Production Data 63
Table 4.1.4 Normality Test of ARCH (1) Rresiduals for the Crude Oil Production Data 64
Table 4.1.5 The ACF and PACF Values for the LTS Crude Oil Production Data 65
Table 4.1.6 Order of ARCH Using the LTS White Test for the Crude Oil Production Data 66
Table 4.1.7 Order of ARCH Using the LTS Breusch-Pagan Test for the Crude Oil Production Data 66
Table 4.1.8 Normality Test of ARCH (1) Rresiduals for the Crude Oil Production Data 67
Table 4.2.1 The ACF and PACF Values for the Total Export of Refined Oil Data 68
Table 4.2.2 Order of ARCH Using the White Test for the Total Export of Refined Oil Data 69
Table 4.2.3 Normality Test of ARCH (1) Rresiduals for the Total Export of Refined Oil Data 70
Table 4.3.1 The ACF and PACF Values for the Export of Crude Oil to North America Data 70
Table 4.3.2 Order of ARCH Using the White Test for the Export of Crude Oil to North America
Data 71
Table 4.3.3 Normality Test of ARCH (2) Rresiduals for the Export of Crude Oil to North America
Data 73
Table 4.4.1 The ACF and PACF Values for the Export of Refined Oil to North America Data 73
Table 4.4.2 Order of ARCH Using the White Test for the Export of Refined Oil to North America
Data 74
Table 4.4.3 Normality Test of ARCH (1) Rresiduals for the Export of Refined Oil to North
America Data 76
Table 4.5.1 The ACF and PACF Values for the Export of Crude Oil to South America Data 76
Table 4.5.2 Order of ARCH Using the White Test for the Export of Crude Oil to South America
Data 77
Table 4.5.3 Normality Test of ARCH (1) Rresiduals for the Export of Crude Oil to South America
Data 79
Table 4.6.1 The ACF and PACF Values for the Export of Crude Oil to South America Data 79
Table 4.6.2 Order of ARCH Using the White Test for the Export of Crude Oil to South America
Data 80
Table 4.6.3 Normality Test of ARCH (1) Rresiduals for the Export of Crude Oil to South America
Data 81
Table 4.7.1 The ACF and PACF Values for the Export of Crude Oil to Western Europe Data 82
Table 4.7.2 Order of ARCH Using the White Test for the Export of Crude Oil to Western Europe
Data 83
Table 4.7.3 Normality Test of ARCH (1) Rresiduals for the Export of Crude Oil to Western
Europe Data 84
Table 4.8.1 The ACF and PACF Values for the Export of Refined Oil to Western Europe Data 85
Table 4.8.2 Order of ARCH Using the White Test for the Export of Refined Oil to Western
Europe Data 86
Table 4.8.3 Normality Test of ARCH (1) Rresiduals for the Export of Refined Oil to Western
Europe Data 87
Table 4.9.1 The ACF and PACF Values for the Export of Crude Oil to Middle East Data 88
Table 4.9.2 Order of ARCH Using the White Test for the Export of Crude Oil to Middle East Data 89
Table 4.9.3 Normality Test of AR (1) Rresiduals for the Export of Crude Oil to Middle East Data 90
Table 4.10.1 The ACF and PACF Values for the Export of Refined Oil to Middle East Data 91
Table 4.10.2 Order of ARCH Using the White Test for the Export of Refined Oil to Middle East
Data 92
Table 4.10.3 Normality Test of AR (1) Rresiduals for the Export of Refined Oil to Middle East
Data 93
Table 4.11.1 The ACF and PACF Values for the Export of Crude Oil to Africa Data 93
Table 4.11.2 Order of ARCH Using the White Test for the Export of Crude Oil to Africa Data 95
Table 4.11.3 Normality Test of AR (1) Rresiduals for the Export of Crude Oil to Africa Data 96
Table 4.12.1 The ACF and PACF Values for the Export of Refined Oil to Africa Data 96
Table 4.12.2 Order of ARCH Using the White Test for the Export of Refined Oil to Africa Data 97
Table 4.12.3 Normality Test of AR (1) Rresiduals for the Export of Refined Oil to Africa Data 98
Table 4.13.1 The ACF and PACF Values for the Export of Crude Oil to Asia and Far East Data 99
Table 4.13.2 Order of ARCH Using the White Test for the Export of Crude Oil to Asia and Far
East Data 100
Table 4.13.3 Normality Test of ARCH (2) Rresiduals for the Export of Crude Oil to Asia and Far
East Data 101
Table 4.14.1 The ACF and PACF Values for the Export of Refined Oil to Asia and Far East Data 102
Table 4.14.2 Order of ARCH Using the White Test for the Export of Refined Oil to Asia and Far
East Data 103
Table 4.14.3 Normality Test of ARCH (1) Rresiduals for the Export of Refined Oil to Asia and
Far East Data 104
Table 4.15.1 The ACF and PACF Values for the Export of Crude Oil to Oceania Data 105
Table 4.15.2 Order of ARCH Using the White Test for the Export of Crude Oil to Oceania Data 106
Table 4.15.3 Normality Test of ARCH (2) Rresiduals for the Export of Crude Oil to Oceania Data 107
Table 4.16.1 The ACF and PACF Values for the Export of Refined Oil to Oceania Data 108
Table 4.16.2 Order of ARCH Using the White Test for the Export of Refined Oil to Oceania Data 109
Table 4.16.3 Normality Test of ARCH (1) Rresiduals for the Export of Refined Oil to Oceania
Data 110
Table 4.17 Selected Models for Saudi Arabia Oil Production Data 111
List of Figures
CHAPTER 1
Figure 1.1 Time Series Plot of Crude Oil Production 5
Figure 1.2 Time Series Plot of Export of Refined Oil 5
Figure 1.3 Time Series Plot of Export of Crude Oil to North America 6
Figure 1.4 Time Series Plot of Export of Refined Oil to North America 6
Figure 1.5 Time Series Plot of Export of Crude Oil to South America 7
Figure 1.6 Time Series Plot of Export of Refined Oil to South America 7
Figure 1.7 Time Series Plot of Export of Crude Oil to Western Europe 8
Figure 1.8 Time Series Plot of Export of Refined Oil to Western Europe 8
Figure 1.9 Time Series Plot of Export of Crude Oil to Middle East 9
Figure 1.10 Time Series Plot of Export of Refined Oil to Middle East 9
Figure 1.11 Time Series Plot of Export of Crude Oil to Africa 10
Figure 1.12 Time Series Plot of Export of Refined Oil to Africa 10
Figure 1.13 Time Series Plot of Export of Crude Oil to Asia and Far East 11
Figure 1.14 Time Series Plot of Export of Refined Oil to Asia and Far East 11
Figure 1.15 Time Series Plot of Export of Crude Oil to Oceania 12
Figure 1.16 Time Series Plot of Export of Refined Oil to Oceania 12

CHAPTER 3
Figure 3.1 Time Series Plot of Original and Missing Value Estimated Export of Crude Oil to
North America 47
Figure 3.2 Time Series Plot of Original and Missing Value Estimated Export of Refined Oil to
North America 48
Figure 3.3 Time Series Plot of Original and Missing Value Estimated Export of Crude Oil to
South America 49
Figure 3.4 Time Series Plot of Original and Missing Value Estimated Export of Refined Oil to
South America 50
Figure 3.5 Time Series Plot of Original and Missing Value Estimated Export of Crude Oil to
Western Europe 51
Figure 3.6 Time Series Plot of Original and Missing Value Estimated Export of Refined Oil to
Western Europe 52
Figure 3.7 Time Series Plot of Original and Missing Value Estimated Export of Crude Oil to
Middle East 53
Figure 3.8 Time Series Plot of Original and Missing Value Estimated Export of Refined Oil to
Middle East 54
Figure 3.9 Time Series Plot of Original and Missing Value Estimated Export of Crude Oil to
Africa 55
Figure 3.10 Time Series Plot of Original and Missing Value Estimated Export of Refined Oil to
Africa 56
Figure 3.11 Time Series Plot of Original and Missing Value Estimated Export of Crude Oil to
Asia and Far East 57