4 CHAPTER
ITEM
TITLE
DECLARATION
DEDICATION
ACKNOLEDGEMENTS
ABSTRACT
ABSTRAK
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
LIST OF APPENDICES
I
II
PAGE
i
ii
iii
iv
v
vi
vii
xi
xii
xiv
xvi
INTRODUCTION
1.1
Introduction
1
1.2
Background of the Study
4
1.3
Statement of the problem
3
1.4
Objectives of the Study
3
1.5
Scope of the Study
4
1.6
Significance of the Study
4
1.7
Summary and Outline of the Proposal Report
4
LITERATURE REVIEW
2.1
Introduction
6
2.2
Gold and its Importance
6
2.3
Gold Forecasting Techniques
7
5 2.4
2.5
III
Forecasting Financial Market Volatility
8
2.4.1 GARCH Models
10
Concluding Remarks
13
RESEARCH METHODOLOGY
3.1
Introduction
14
3.2
Linearity of the Series
14
3.3
Test for the Stationarity
15
3.4
Univariate Box- Jenkins Models
16
3.4.1 Mixed Autoregressive-Moving Average Model
16
3.4.2 Autoregressive Integrated Moving Average Model 17
3.5
Modeling of volatility
3.5.1
18
Autoregressive Conditional Heteroscedastic Model 18
3.5.1.1 Lagrange Multiplier Test
19
3.5.2 GeneralisedAutoregresssive Conditional
Heterocedastic Model.
3.6
20
3.5.2.1 Parameter Estimation of GARCH
21
3.5.2.2 Test of normality
23
3.5.2.3 Diagnostic Checking
24
3.5.2.4 Checking the Adequacy
25
3.5.3 GARCH ( 1 , 1 ) Models
26
3.5.4 Exponential GARCH
27
Forecasting
28
3.6.1 Forecast of ARIMA models
28
3.6.2 Forecast of ARCH models
28
3.6.3 Forecast of GARCH models
29
3.6.4 Forecast of GARCH (1,1) models
30
6 IV
V
3.6.5 Forecast of EGARCH models
31
3.7
Measures of performance
31
3.8
Operational Framework
32
DATA ANALYSIS
4.1
Introduction
34
4.2
Data analyses
34
4.3
Data Modeling
35
4.3.1 Analyses of Data using Box-Jenkins Model
35
4.3.2 Testing for Stationarity
37
4.3.3 Model Identification
38
4.3.4 Parameter Estimations of ARIMA Model
40
4.3.5 Analyses of Data using GARCH Model
41
4.3.5.1 Testing for volatility
41
4.3.5.2 Parameter Estimation of ARCH Model
44
4.3.5.3 Parameter Estimation of GARCH Model
44
4.3.5.4 Parameter Estimation of EGARCH Model
45
4.4
Performance Measure
46
4.5
Concluding Remarks
47
DISCUSSION OF RESULTS
5.1
Introduction
48
5.2
Prediction of Gold Prices using the GARCH model
48
5.3
Forecast gold price using ARIMA Models
48
5.4
Forecast gold price using GARCH Models
50
5.5
Comparison between GARCH and ARIMA
Models in Forecasting Gold Prices
54
7 5.6
VI
Concluding Remarks
55
CONCLUSIONS AND SUGGESTIONS
6.1
Introduction
56
6.2
Summary and Conclusions of the study
56
6.3
Suggestion for Future Study
57
59
REFERENCES
APPENDICES
Appendix A
64
LIST OF FIGURES
8 FIGURE NO.
ITEM
PAGE
3.1
Linear Trend
15
4.1
Gold Prices from 4 Jan 2000 until 12 March 2010.
35
4.2
Graph of stationary
37
4.3
Autocorrelation Function (ACF) for d=1
38
4.4
Partial Autocorrelation Function (PACF) for d=1
39
4.5
Graph of forecasting gold price of ARIMA (1,1,3)
41
4.6
Variance not constant
41
4.7
Volatility clustering
42
4.8
Normality Graph
43
4.9
Forecasting Graph of variance of ARCH (1)
44
4.10
Forecasting Graph of variance of GARCH (1,3)
45
4.11
Forecasting Graph of variance of EGARCH (1,3)
46
5.1
Graph of forecasting ARIMA (1, 1, 3)
50
5.2
Graph of forecasting GARCH (1,3)
52
5.3
Graph of forecast of variance of GARCH (1,3)
52
5.4
Graph of forecasting EGARCH (1,3)
53
5.5
Graph of forecast of variance of EGARCH (1,3)
53
9 LIST OF SYMBOL
10 t
-
time
-
conditional variance
p
-
lag order of the autoregressive
q
-
lag order of the moving average
d
-
difference of model
α
-
parameter equation
β
-
parameter equation
(B) -
autoregressive operator of order p
(B) -
moving average operator of order q
-
equation in time
-
mean
-
delta
1
B
S -
shock at time t
-
backward shift operator
-
conditional mean
-
residual error
-
likelihood of
-
pi
‐ skewness n ‐ dth difference
.
number of observations -
kurtosis
-
sample mean
-
variance
-
portmanteau test
11 T
-
number of observations in portmanteau test
log
-
log conditional variance
-
gamma
-
forecast of a t time
LIST OF APPENDICES
12 APPENDIX
A
TITLE
Gold price data in Australian dollar from 4 January
2000 until 14 March 2010.
CHAPTER 1
PAGE
64