Download Stock Return and the Volatility Persistence in the Nigerian Capital

STOCK RETURN AND THE VOLATILITY PERSISTENCE IN THE
NIGERIAN CAPITAL MARKET
BY
SULEIMAN, Hamisu Kargi
PhD./ADMIN/11934/2008-2009
Being a Seminar Paper submitted to the Department of Accounting,
Ahmadu Bello University, Zaria as part of the requirement for
PhD. Accounting and Finance.
JULY, 2011
1
ABSTACT
Investment in capital market is always surrounded with uncertainty of what return may be
particularly in the emerging economies. A rational person makes investment with some
expectation of returns and a fall in stock prices weaken consumer confidence and drive down
consumer spending. Stock market volatility affects business investment and economic growth.
The degree of volatility presence in the stock market would lead investors to demand a higher
risk premium, creating higher cost of capital, which impedes investment and slows economic
development. The study addresses the robustness of stock return volatility and its effect on the
performance on the Nigerian capital market. The study is both descriptive and historical in
nature and utilises daily market capitalization index of the Nigeria Stock Exchange (NSE) for the
period of trading 21st April, 2008 to 8th June, 2011. Autoregressive conditional
heteroskedasticity (ARCH) model and its extension the generalised autoregressive conditional
heteroskedasticity (GARCH) model was used to estimate the conditional variance of Nigeria’s
daily stock return. The results show the volatility presence in the conditional variance of the
market return and a long-term volatility persistent in the stock market of Nigeria indicating
market inefficiency. Base on the findings, there is need for the modernization of the Nigerian
Stock Exchange to improve the trading system and development of specialized financial
institutions (portfolio managers) to permit dissemination of company specific information to the
investors. This will improve market efficiency in Nigeria.
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BACKGROUND TO THE STUDY
Understanding stock market risk and return behaviour is important for all countries but it
is of more importance to developing countries especially where the market consist of risk–averse
investors as the opportunities to invest and diversify the investment is not much. The degree of
volatility presence in the stock market would lead investors to demand a higher risk premium,
creating higher cost of capital, which impedes investment and slows economic development. A
common problem plaguing the low and slow growth of developing economies is the shallow
financial sector. Financial markets play an important role in the process of economic growth and
development by facilitating savings and channelling funds from savers to investors. While there
have been numerous attempts to develop the financial sector, emerging economies are also
facing the problem of high volatility in numerous fronts. Volatility may impair the smooth
functioning of the financial system and adversely affect economic performance.
Similarly, stock market volatility also has a number of negative implications. One of the
ways in which it affects the economy is through its effect on consumer spending (Campbell,
1996; Starr-McCluer, 1998; Ludvigson and Steindel 1999 and Poterba 2000). The impact of
stock market volatility on consumer spending is related via the wealth effect. Increased wealth
will drive up consumer spending. However, a fall in stock market will weaken consumer
confidence and thus drive down consumer spending. Stock market volatility may also affect
business investment (Zuliu, 1995) and economic growth directly (Levine and Zervos, 1996 and
Arestis et al 2001). A rise in stock market volatility can be interpreted as a rise in risk of equity
investment and thus a shift of funds to less risky assets. This move could lead to a rise in cost of
funds to firms and thus new firms might bear this effect as investors will turn to purchase of
stock in larger, well known firms.
While there is a general consensus on what constitutes stock market volatility and, to a
lesser extent, on how to measure it, there is far less agreement on the causes of changes in stock
market volatility. Some economists see the causes of volatility in the arrival of new,
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unanticipated information that alters expected returns on a stock (Engle and Ng, 1993). Thus,
changes in market volatility would merely reflect changes in the local or global economic
environment. Volatility is caused mainly by changes in trading volume, practices or patterns,
which in turn are driven by factors such as modifications in macroeconomic policies, shifts in
investor tolerance of risk and increased uncertainty.
The degree of stock market volatility can help forecasters predict the path of an
economy’s growth and the structure of volatility can imply that “investors now need to hold
more stocks in their portfolio to achieve diversification”(Krainer, 2002). This case is more
serious for developing economies like Nigeria that is attempting to deepen its financial sector by
developing its stock market. Unlike matured stock markets of advanced economies, the Nigerian
stock market began to develop rapidly only in the last two decades and is sensitive to factors
such as changes in the levels of economic activities, changes in the political and international
economic environment and also related to changes in the macro economic variables. Therefore,
this paper examine whether Nigeria’s Stock market is volatile.
The study primarily addresses the robustness of stock return volatility and its effect on
the performance on the Nigerian capital market. What is the characteristic of stock return
volatility in the Nigerian capital market? Does the stock return volatility affect the
operation/performance of the Nigerian capital market? In line with the stated objective and
questions raised, the hypothesis is that stock return volatility is not persistent in the Nigerian
capital market.
The second section of the paper provides an overview of related literature and the third
section presents an exposition of the methodology used in the study. The fourth section provides
the results and its discussion. The last section provides a summary and conclusion.
4
LITERATURE REVIEW
Volatility is one of the important aspects of financial market developments providing an
important input for portfolio management, option pricing and market regulations (Poon and
Granger, 2003). Stock returns volatility differs dramatically across international markets (Xing,
2004; Roll, 1992; Harvey, 1995, Bekaert and Harvey, 1997; and Aggarwal et al. 1999) and have
received a great attention from both academicians and practitioners over the last two decades
because it can be used as a measure of risk in financial markets. Volatility of stock returns has
long been an issue of interest in financial literature. A wide variety of research has been
conducted on stock returns volatility in developed and emerging markets since 1970s. Nature of
volatility in different markets at different times are discovered, which are indeed of great interest
for financial economists. Financial economists are also interested about the causes and variables
behind the existence and nature as well as the anomalies relating to market volatility.
In the financial econometrics literature, empirical evidence presented by Donaldson and
Kamstra (1997) suggest that stock return volatility is asymmetrically related to past return, with
negative unexpected returns. Koutmos (1999) provides evidence that, in agreement with
developed markets, stock returns volatility in emerging markets adjust asymmetrically to past
information. Studying the Korea and Taiwan stock markets, Titman and Wei (1999) find that
Taiwanese stock returns volatility are more correlated with their earnings than Korean returns
volatility. The asymmetry argument suggests that the local factors rather than the external factors
drive national stock market returns volatility. Harvey (1995) provides evidence that volatility in
emerging equity markets is less than in developed equity markets.
Focusing on the forces that determine volatility, Bekaert and Harvey (1997) find in fully
integrated markets, volatility is strongly influenced by the local and the world factors while in
segmented capital markets, volatility is more likely to be influenced by the local factors. They
argue that political risk measured by low credit rating and unstable macroeconomic policies
might be translated into high stock market returns volatility. Examining the cause of return
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volatility in a small and internationally integrated stock market using the Irish equity market,
Kearney (1998) finds that the volatility of the exchange rate is a more significant determinant of
the Irish equity market return volatility than the global factors. Aggarwal et al, (1999)
investigate which events causes volatility of emerging stock market returns by examining the
global and local events (social, political, and economic) during the period of increased volatility
and find that most events tend to be local.
Recently, authors started to look at country-specific risk in addition to the world risk in
order to explain the local factors that cause stock market returns volatility. Erb, et al. (1995) find
that country risk measures have substantial predictive power for stock market return volatility. In
another study by Erb, et al. (1996), country financial risk measured by country credit rating is
found sufficient to explain the emerging markets’ stock return volatility but insufficient to
explain the volatility of returns in developed markets. Cohen et al.'s (1976) observe that
differences in return volatility as because of market thinness and share turnover. Emerging
Markets are characterized by high risk and return, highly unpredictable and high volatility
compared to the developed markets (Bekaert and Harvey, 1997). Diamonte, Liew, and Viskanta
(1996) quantify the importance of political risk in predicting volatility in emerging and
developed markets. The leading result of this study is that changes in political risk have a more
pronounced impact on the emerging markets’ return volatility than on developed markets’ return
volatility.
The empirical evidence of existing studies vary a large extent among the researchers but
there is a unanimity among researchers that the issue of stock returns volatility is important. The
empirical studies on stock return and volatility has been focused on different angles of risk
return relationship and volatility persistence shocks. Batra (2004) investigated Indian stock
market from 1979 -2003 and concluded that stock return volatility persistence was increasing on
account of financial liberalization process. Persistency is found to be the characteristics of each
and every stock market of the world. Floros (2008) found persistence for Egypt and Israel stock
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markets and concluded that long run component converges slowly. The volatility varies from
time to time, and for different frequency, it shows a different pattern, as Caiado (2004) found
that the conditional volatility of the stock returns was more persistent in daily series than the
low-frequency series. Stock market has characteristic that high volatility periods tend to be
persistent. In this study different frequency data are used for investigating this phenomenon of
the volatility persistency. Thomas (1995) used GARCH model and estimated strong persistence
in variance for daily, weekly and monthly stock returns. In monthly returns, he found seasonality
in the volatility and there was one regime shift in the data. Dawood (2007) investigated volatility
in the Karachi stock exchange and found that in 1990’s market had become more volatile on
short as well as medium term basis. He found that the stock market reacted too actively to
economic shocks, but this reaction took place on a daily basis and die away within a month.
Several studies such as Haque and Hassan (2000), Harvey (1995a, 1995b), Harvey and
Bekaert (1997), Bekaert (1995), Kim and Singal (1999), Choudhury (1996), Lee and Ohk
(1991), and Classens et al. (1995) reveal the evidence of market volatility in the emerging stock
markets. The financial literature that offers research on stock market volatility over time and
linkages that exist among world markets is still unresolved. Theoretical works by (Whitelaw,
2000, Bekaert and Wu, 2000; and Wu, 2001) consistently assert that stock market volatility
should be negatively correlated with stock returns. Earlier study of French et al. (1987) found a
positive and significant relationship. However, studies such as Baillie and DeGennaro (1990);
Theodossiou and Lee (1995) reported a positive but insignificant relationship between stock
market volatility and stock returns. Consistent with the asymmetric volatility argument,
researches recently report negative and often significant relationship between the volatility and
return (Nelson, 1991, Glosten et al., 1993, Bekaert and Wu, 2000, Wu, 2001; Brandt and Kang,
2003).
It has been empirically demonstrated that the relationship between return and volatility
depends on the specification of the conditional volatility. In particular, using a parametric
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GARCH-M model, Li (2002) finds that a positive but statistically insignificant relationship
exists. In contrast, using a flexible semi-parametric GARCH-M model, the study document that
a negative relationship prevails instead. While the volatility for the stock market as a whole has
been remarkably stable over time, the volatility of individual stocks appears to have increased.
Li (2002) examined the relationship between expected stock returns and volatility in the twelve
largest international stock markets. Consistent with the most previous studies, they found the
estimated relationship between return and volatility sensitive to the way volatilities are
examined. However, Batra (2004) examined the time variation in volatility in the Indian stock
market. He used the asymmetric GARCH methodology augmented by structural changes. Batra
identifies sudden shifts in the stock price volatility and nature of events that cause these shifts in
volatility.
Selcuk (2004) investigated volatility in emerging stock markets and found volatility
persistency and high volatility in the developing markets. GARCH parameters are able to
explain the level of persistency in the volatility. Magnus and Fosu (2006) found the parameter
estimates of GARCH models close to unity and suggested a high level of persistence in the
Ghana stock exchange.
Non linear models are considered to be the dominant models than the linear class of
models. Rashid and Ahmad (2008) investigated a class of models and found that the nonlinear
GARCH models dominate the other class of models in predicting stock market volatility in
Pakistan. Ali and Akbar (2007) used data from 1991 to 2006 and applied one Factor ANOVA
and found that weekly and monthly effects did not show inefficiency in stock returns of
Pakistani equity market, however, the market is inefficient in the short run (daily effects).
Persistency in volatility is normally due to the inefficiency in the market. Market is said
to be volatile past prices reflect in the future prices. Rizwan and Khan (2007) studied the
volatility of the Pakistani stock market and found persistence, which signified inefficiency in the
stock market. They found that lagged returns in the GARCH model were significant in
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explaining current returns. Amir and Kashif-Ur-Rehman (2011) compare the variance structure
of high (daily) and low (weekly, monthly) frequencies of data of the Pakistani stock market. By
employing ARCH (1) and GARCH (1, 1) models, the study found that statistical properties of
the three data series of returns were substantially different from one another. The presence of
persistency was more in the daily stock returns as compared to other data sets, which showed
that the volatility models were sensitive to the frequencies of data series.
In Nigeria, studies on modelling volatility of stock returns provide different perspectives.
Jayasuriya (2002) use asymmetric GARCH methodology to examine the effect of stock market
liberalization on stock returns volatility of fifteen emerging markets, including Nigeria, for the
period December 1984 to March 2000. The study reports, among others, that positive (negative)
change in prices have been followed by negative (positive) changes indicating a cyclical type
behavior in stock price changes rather than volatility clustering in Nigeria. Ogum, et al., (2005)
investigate the emerging market volatility using Nigeria and Kenya stock return series. Their
results of the exponential GARCH model indicate that asymmetric volatility found in the U.S.
and other developed markets is also present in Nigerian, but Kenya shows evidence of
significant and positive asymmetric volatility, suggesting that positive shocks increase volatility
more than negative shocks of an equal magnitude.
Olowe (2009) investigated the relation between stock returns and volatility in Nigeria
using E-GARCH-in-mean model in the light of banking reforms, insurance reform, stock market
crash and the global financial crisis. His findings found little evidence on the relationship
between stock returns and risk as measured by its own volatility and show that banking reform
and stock market crash negatively impacts on stock return while insurance reform and the global
financial crisis have no impact on stock return.
More recently, Emenike (2010) uses Monthly All Share Indices to investigate volatility
persistence, asymmetric properties of the series and leverage effects in Nigeria. The results of
GARCH (1,1) model indicate evidence of volatility clustering in the NSE return series. Also, the
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results of the GJRGARCH (1,1) model show the existence of leverage effects in the series.
Overall results from this study provide evidence to show volatility persistence, fat-tail
distribution, and leverage effects for the Nigeria stock returns data.
However, in finance literature price changes represent random departure from previous
and are known as random walk. Random walk is associated with efficient market hypothesis
EMH and follow were information is unimpeded and information is immediately reflected in
stock prices, then tomorrow’s price change will reflect only tomorrow’s news and will be
independent of the price changes today (Burton, 2003). But news is by definition unpredictable
and, thus, resulting price changes must be unpredictable and random.
Persistency is related to the jumps, which changes the volatility pattern for a reasonable
time period. Long memory and persistence is related with the longer movement in the returns
series. A significant impact of volatility on the stock prices can only take place if shocks to
volatility persist over a long time (Poterba and Summers, 1986). As Maheuy and McCurdyz
(2003) modelled the jump dynamics and volatility components, he concluded that no jump takes
a significant period of time to return to normal level. The persistency in volatility is due to
different reasons and it varies from country to country and time to time. There are little empirical
evidences available for Nigerian market regarding volatility characteristic. This study fills this
gap by capturing this important phenomenon of stock returns volatility and ascertain whether
Nigerian capital market is relevant.
This study attempts to investigate the insight into the risk return relationship,
predictability, and volatility persistence shocks in Nigeria using daily data which might be
helpful for risk management through portfolio management.
METHODOLOGY
This study is both descriptive and historical in nature as it seeks to describe the pattern of
returns of the Nigerian Stock Exchange (NSE) in the past. Data collected was the daily market
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capitalization index of the NSE for the period of trading 21st April, 2008 to 8th June, 2011. The
period was chosen base on the data available in the Cowry Asset Managers website and
comprises of 757 observations. To improve interpretability the data was transformed by means
of natural logarithm. The autoregressive conditional heteroskedasticity (ARCH) model
introduced by Engle (1982) and its extension, the generalised autoregressive conditional
heteroskedasticity (GARCH) model (Bollerslev, 1986), was used to estimate the conditional
variance of Nigeria’s daily stock return. This method allows for an objective determination of
the presence of volatility. ARCH models and its extension, the GARCH models have been the
most commonly employed class of time series models in the recent finance literature for
studying volatility. The appeal of the models is that it captures both volatility clustering and
unconditional return distributions with heavy tails. The estimation of GARCH model involves
the joint estimation of a mean and a conditional variance equation. According to the GARCH (p,
q) model, the conditional variance of a time series depends on the squared residuals of the
process. In this study the model were based on autoregressive AR(1) estimation of the residuals.
The autoregressive model is thus
It = a0 + a1It - 1 + ut
Where; It = market index at time t
It – 1 = market index at time t – 1
a0 = intercept
a1 = coefficient of the market index at time t - 1
ut = stochastic error term
In the model the value of I at time t depends on its value in the previous time period and
a stochastic error term. Both ARCH and GARCH models were based on the regression of
squared error term. Under the ARCH model, the ‘autocorrelation in volatility’ is modeled by
allowing the conditional variance of the error term, σ2t, to depend on the immediately previous
value of the squared error.
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σ2t = ω + α1u2t − 1
The GARCH model allows the conditional variance to be dependent upon conditional
variance lags, so that the conditional variance equation is now
σ2t = ω + αu2t − 1 + βσ2t − 1
where; ω = constant term,
αu2t-1 = ARCH term
βσ2t-1 = GARCH term
ARCH and GARCH models have been applied to a wide range of time series analysis,
but applications in finance have been particularly successful (Engle, 2001). This study employs
GARCH (1,1), type model has been computed with the aid of Eviews software. The study hold
the views of Engle and Bollerslev (1986), Chou (1988), and Bollerslev et al. (1992) where they
show that the persistence of shocks to volatility depends on α + β parameters. Where α + β < 1
imply a tendency for the volatility response to decay over time, α + β = 1 imply indefinite
volatility persistence to shocks over time, and α + β > 1 imply increasing volatility persistence
over time and covariance stationarity is violated. In addition, Hasan et. al (2000) indicate that
significance of [alpha] parameter signals the tendency of shock to persist.
RESULTS AND DISCUSSION
The mean of the data – daily market capitalisation index (MKTINDEX) in the Nigerian
Stock Exchange (NSE) during the period of the study [appendix I(a)] is 29664.48 while the
standard deviation of the index series is 11180.32. However, the Skewness of this study is
1.732125 and the Kurtosis is 4.649964, suggest non-normality of the market. Jarque-Bera test
also reject the normality of the data at 1% level (464.4009) being higher than the X2-value of
5.99 and 9.21 at 5% and 1% respectively. Overall, the non-normality of the index series revealed
in this study suggests using non-linear model.
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The stationarity test of the logged data (LOGMKTINDEX) indicate the presence of unit
root in the level test as shown by the Augmented Dickey Fuller ADF -2.581105 showing nonstationarity at both 1% and 5% [appendix I(b)]. However, the first difference ADF (-13.96995)
depict stationarity in the data residuals [appendix I(c)]. Equally, correlograms and Q-statistics
first difference tests further shows stationarity in the residuals and are serially correlated
(appendix II). The correlogram test the presence of ARCH effect in the data.
Autocorrelation is the measure of persistence and/or predictability of the market returns
based on past market returns. The coefficient of the first order auto-correlation AR(1) is
0.993745 (appendix III) indicating that market returns in the NSE are predictable on the basis of
past returns. Accordingly, this rejects the Efficient Market Hypothesis. The departure from the
efficient market hypothesis of the NSE suggests that relevant market information is only
gradually reflected in stock price changes. This arises from frictions in the trading process,
limited provision of information of firm’s performance to market participants.
The result in appendix III shows that GARCH (1,1) model is thus,
σ2t = 0.0000378 + 0.524537u2t − 1 + 0.302744σ2t − 1
The ARCH coefficient is 0.524537 and significant at 1% level implies the tendency of
the shock to persist. The ARCH coefficient is significantly positive though not close to one and
indicates an integrated ARCH process in which shocks have a persistent effect on volatility. The
ARCH term shows that the current period volatility is dependent on the lagged error terms. The
GARCH coefficient for the model 0.302744 is highly significant in the Nigeria stock market and
implies persistent shocks in the NSE. This shows that the past variance terms have a strong
impact on the current conditional variance and exhibit that the last period’s volatility has a
significant impact on the current period conditional volatility. The residual graph (appendix IV)
depicted volatility in the residuals, showing clustering in the daily percentage change in the log
of NSE market index. The results support the evidence of volatility clustering in Nigeria
13
provided by Ogum, et al., (2005) and Emenike (2010). This is also similar to the findings of
French et al. (1987), Harvey (1995), Li (2002) and Batra (2004).
Despite the significance of α and β coefficients and volatility persistence parameter α + β
is close to 1 (0.827281). In GARCH-type model that indicates the tendency for volatility
response to shocks to display a long memory in the NSE, base on this result the null hypothesis
that stock return volatility is not persistence in Nigeria is rejected. The high persistence
(0.827281) shows that the volatility of the stock returns dies down slowly. The results indicate
high volatility presence in the conditional variance therefore market returns depend on their own
shocks and confirm the volatility clustering phenomenon for the inefficient market as also found
by Rizwan and Khan (2007) that the volatility clustering exists for Pakistani stock market, which
signifies inefficiency in the stock market. These results clearly explain the volatile nature of
emerging markets and provide clear evidence of time varying risk in the emerging stock market
of the NSE.
The significance of the conditional variance coefficient revealed by GARCH (1, 1)
model implies long-term volatility persistent in the stock market of Nigeria. This may be the
cause of frictions in the securities market trading. This result also indicate that the participants
may have limited access to the market information regarding the firms performance either
because the firms do not make available their financial statements timely or investors do not
seek financial advice in stock dealings due to lack of professional financial community who can
analyze stock market data for the investors. Persistency in volatility is normally due to the
inefficiency in the market.
In addition, market inefficiency may be the result of non-synchronous effects, which
implies that information in the stock market is processed with a lag. The study presented a
positive autocorrelation which may implies non-enforcement of regulations and/or weak
supervision by the Securities and Exchange Commission (SEC), however, Cambell et al. (1997)
noted that non-synchronous trading is caused by negative autocorrelation in portfolio returns.
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Further, the findings might has implications on investors in Nigeria as volatility in the stock
return of a firm stems from the fact that stock returns may no longer be seen as the true intrinsic
value of a firm and thus the investors might start losing confidence in the stock market.
CONCLUSION AND RECOMMENDATION
This study investigates the time-varying risk return relationship within GARCH
framework and the persistence of shocks to volatility in the stock market of Nigeria. Using
GARCH type models, it reveals that NSE is volatile and there is a persistence shocks in the
market like in other emerging markets. The study employ daily data of large sample size and
reveals the risk return characteristics and volatility persistence shocks in the emerging stock
market of Nigeria indicating inefficient market. Therefore, there is need for the modernization of
the Nigerian Stock Exchange to improve the trading system to permit immediate information
dissemination to investors and there is need for the development of specialized financial
institutions (portfolio managers) who can analyze stock market data for the investors so as to
speed off adjustment to new information arrival. Finally, timely disclosure and appropriate
dissemination of company specific information to the investors will also improve the efficiency
of the stock market in Nigeria.
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19
APPENDIX 1
a) DESCRIPTIVE STATISTICS
Date: 07/07/11
Time: 16:07
Sample: 4/21/2008 6/08/2011
MKTINDEX
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
29664.48
25269.36
62711.56
19814.92
11180.32
1.732125
4.649964
Jarque-Bera
Probability
464.4009
0.000000
Sum
Sum Sq. Dev.
22456014
9.45E+10
Observations
757
Source: Eviews result output
b) LEVEL AUGMENTED DICKEY-FULLER TEST
Null Hypothesis: LOGMKTINDEX has a unit root
Exogenous: Constant
Lag Length: 2 (Automatic based on SIC, MAXLAG=19)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
t-Statistic
Prob.*
-2.581105
-3.438796
-2.865158
-2.568752
0.0973
*MacKinnon (1996) one-sided p-values.
Source: Eviews result output
c) FIRST DIFFERENCE AUGMENTED DICKEY-FULLER TEST
Null Hypothesis: D(LOGMKTINDEX) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=19)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
t-Statistic
Prob.*
-13.96995
-3.438796
-2.865158
-2.568752
0.0000
*MacKinnon (1996) one-sided p-values.
Source: Eviews result output
20
APPENDIX II
CORRELOGRAM OF FIRST DIFFERENCE [D(LOGMKTINDEX)]
Date: 07/14/11 Time: 06:45
Sample: 4/21/2008 6/08/2011
Included observations: 756
Autocorrelation
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Partial Correlation
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
AC
PAC
Q-Stat
Prob
0.574
0.263
0.081
0.011
-0.053
-0.051
-0.037
-0.049
-0.023
0.061
0.098
0.093
0.106
0.076
-0.004
-0.030
-0.016
-0.048
-0.044
-0.039
0.026
0.055
0.070
0.091
0.103
0.117
0.122
0.094
0.030
-0.051
-0.071
-0.082
-0.064
-0.069
-0.058
-0.028
0.041
0.110
0.097
0.093
0.073
-0.012
-0.057
-0.045
-0.038
-0.046
-0.036
0.016
0.020
0.033
0.574
-0.099
-0.042
0.006
-0.068
0.021
-0.006
-0.044
0.036
0.095
0.017
0.011
0.060
-0.022
-0.064
0.022
0.015
-0.057
0.026
-0.027
0.076
0.016
0.001
0.045
0.043
0.057
0.036
0.010
-0.027
-0.067
0.006
-0.035
-0.002
-0.051
-0.026
0.016
0.063
0.049
-0.028
0.054
0.019
-0.083
0.008
0.029
-0.021
-0.013
-0.008
0.032
-0.033
-0.008
250.04
302.63
307.64
307.73
309.87
311.83
312.89
314.74
315.14
318.00
325.46
332.17
340.87
345.39
345.41
346.09
346.29
348.04
349.53
350.71
351.24
353.56
357.39
363.84
372.11
382.93
394.60
401.53
402.26
404.29
408.28
413.58
416.87
420.62
423.34
423.98
425.33
435.03
442.55
449.52
453.78
453.89
456.51
458.14
459.28
460.99
462.06
462.27
462.60
463.47
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Source: Eviews result output
21
APPENDIX III
AUTOREGRESSIVE AR(1), AUTOREGRESSIVE CONDITIONAL
HETEROSKEDASTICITY [ARCH(1)] AND THE GENERALISED AUTOREGRESSIVE
CONDITIONAL HETEROSKEDASTICITY [GARCH(1)] RESULT
Dependent Variable: LOGMKTINDEX
Method: ML - ARCH (BHHH)
Date: 07/08/11 Time: 17:03
Sample(adjusted): 4/22/2008 6/08/2011
Included observations: 756 after adjusting endpoints
Convergence achieved after 28 iterations
Variance backcast: ON
C
AR(1)
Coefficient
Std. Error
z-Statistic
Prob.
10.01856
0.993745
0.082295
0.001271
121.7392
782.0906
0.0000
0.0000
9.604297
7.171704
5.354992
0.0000
0.0000
0.0000
Variance Equation
C
ARCH(1)
GARCH(1)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
Inverted AR Roots
3.78E-05
0.524537
0.302744
0.998094
0.998084
0.013368
0.134198
2308.595
0.858074
3.93E-06
0.073140
0.056535
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
.99
Source: Eviews result output
22
10.24285
0.305396
-6.094168
-6.063559
98328.06
0.000000
APPENDIX IV
RESIDUAL GRAPH
.06
.04
.02
.00
-.02
-.04
-.06
-.08
-.10
08:07
09:01
09:07
10:01
10:07
LOGMKTINDEX Residuals
Source: Eviews result output
23
11:01