vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLES OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xii
LIST OF APPENDICES
xiv
INTRODUCTION
1
1.0
Introduction
1
1.1
Background of Study
2
1.2
Problem Statements
4
1.3
Research Objective
6
1.4
Research Questions
6
1.5
Scope of the Study
7
1.6
Significance of the Study
7
1.7
Organisation of the Report
8
LITERATURE REVIEW
9
2.0
Introduction
9
2.1
Dynamic Regression Model
9
2.2
Autoregressive
Distributed
Lag
(ARDL)
11
viii
Model
3
2.3
Related Studies on ARDL
13
2.4
Related Studies on Palm Oil Price
19
2.5
Summary
23
RESEARCH METHODOLOGY
26
3.0
Introduction
26
3.1
Testing for Stationarity
26
3.2
ARDL model
29
3.2.1 Model Specification
30
3.2.2 ARDL Bound Test for Cointegration
30
3.2.3 Expressing ARDL Model as Error
31
Correction Model (ECM)
3.2.4 Estimation of the Long-run
33
Coefficients
3.2.5 Choosing Lag Length on First
35
Difference Variables
3.2.6 Estimation of ARDL model
37
Box-Jenkins ARIMA model
37
3.3.1 Stationary Time Series Model
38
3.3.2 Non-Stationary Time Series Model
39
3.3.3 Model Identification
40
3.3.4 Parameter Estimation
41
Model Diagnostic
45
3.4.1 Stability Test
46
3.5
Model Evaluation
49
3.6
Operational Framework
51
3.7
Summary
54
3.3
3.4
4
DATA ANALYSIS
55
4.0
Introduction
55
4.1
Data Description
55
4.2
Analysis by using ARDL model
59
ix
4.2.1 Stationary Testing
59
4.2.2 Existence of the Long-run Relationship
69
4.2.3 Estimation of the ARDL model
70
4.2.4 Estimation of the Long-run
74
Coefficients
4.2.5 Estimation of the Error Correction
76
Model
4.3
4.4
4.2.6 Model Diagnostics
78
Analysis by using ARIMA model
81
4.3.1 Stationary Testing
82
4.3.2 Model Identification
84
4.3.3 Parameter Estimation
86
4.3.4 Model Diagnostics
88
Data Modelling
89
4.4.1 Modelling using ARDL (2,2,0,0,2)
89
4.4.2 Modelling using ARDL (1,2,0,0,2)
91
4.4.3 Modelling using ARIMA (1,1,6)
92
4.4.4 Modelling Performances of ARDL
93
and ARIMA Model
4.5
5
Summary
94
CONCLUSION AND RECOMMENDATIONS
95
5.0
Introduction
95
5.1
Summary
95
5.3
Conclusions
96
5.3
Suggestion for Future Study
98
REFERENCES
Appendices A – B
101
106-131
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
Summary of studies for ARDL model
23
4.1
ADF test of the logarithmic price at level
60
4.2
ADF test of the logarithmic price at first difference
61
4.3
ADF test of the logarithmic production at level
62
4.4
ADF test of the logarithmic production at first
63
difference
4.5
ADF test of the logarithmic import at level
65
4.6
ADF test of the logarithmic export at level
66
4.7
ADF test of the logarithmic stock at level
67
4.8
Integrating order of all the logarithmic variables
68
4.9
F-statistics for testing the existence of a long-run price
70
equation
4.10
Estimated ARDL (2,2,0,0,2)
71
4.11
Estimated ARDL (1,2,0,0,2)
72
4.12
Long-run coefficients estimates for ARDL (2,2,0,0,2)
74
4.13
Long-run coefficients estimates for ARDL (1,2,0,0,2)
75
4.14
Error correction representation of ARDL Model 1
76
4.15
Error correction representation of ARDL Model 2
77
4.16
ADF test of the original data for price
82
4.17
ADF test of the price at first difference
83
4.18
Possible ARIMA models for price
85
4.19
Equations of ARIMA (p,d,q) for price
86
xi
4.20
Summary of Q-statistics for ARIMA model
88
4.21
Corresponding AIC for the adequate model
88
4.22
Modelling performance of ARDL (2,2,0,0,2)
90
4.23
Modelling performance of ARDL (1,2,0,0,2)
92
4.24
Modelling performance of ARIMA (1,1,6)
93
4.25
Modelling performance of ARDL and ARIMA models
93
5.1
Modelling performance of ARDL and ARIMA models
98
xii
LIST OF FIGURES
FIGURE NO.
3.1
TITLE
PAGE
The process in developing an ARDL model using
52
ARDL bound test
3.2
The process in developing an ARIMA model
53
4.1
Monthly prices of crude palm oil from January 2000
56
until December 2013
4.2
Monthly production of crude palm oil from January
57
2000 until December 2013
4.3
Monthly import volume of crude palm oil from
57
January 2000 until December 2013
4.4
Monthly export volume of crude palm oil from
58
January 2000 until December 2013
4.5
Monthly closing stock of crude palm oil from
58
January 2000 until December 2013
4.6
Asymptotic critical value bounds for the F-statistic
69
for Case III (unrestricted intercepts; no trends)
4.7
ACF, PACF and Q-statistics of the residuals for
78
ARDL (2,2,0,0,2)
4.8
ACF, PACF and Q-statistics of the residuals for
79
ARDL (1,2,0,0,2)
4.9
Plot for a) CUSUM and b) CUSUMQ of the
80
recursive residual for ARDL (2,2,0,0,2)
4.10
Plot for a) CUSUM and b) CUSUMQ of the
recursive residual for ARDL (1,2,0,0,2)
80
xiii
4.11
ACF and PACF for price at first difference level
85
4.12
Modelling graph for palm oil price using ARDL
90
(2,2,0,0,2)
4.13
Modelling graph for palm oil price using ARDL
91
(1,2,0,0,2)
4.14
Modelling graph for palm oil price using ARIMA
(1,1,6)
92
xiv
LIST OF APPENDICES
APPENDIX
A
TITLE
Monthly price, production, closing stock,
PAGE
106
import and export volume of palm oil
B
All ARDL and ARIMA models involved in
modelling palm oil price
121