INTRODUCTION
Volatility is a key concept in finance, representing the unpredictability and risk associated with asset returns It is measured through standard deviation or variance, serving as a proxy for risk in financial markets Recent years have seen significant volatility in both mature and emerging markets, prompting extensive research by academics and practitioners on modeling and forecasting stock market volatility Such fluctuations can greatly affect risk-averse investors, influencing their consumption patterns, corporate investment decisions, and overall business cycles Additionally, accurate volatility forecasts are essential for pricing derivatives and formulating effective trading and hedging strategies, making it crucial to comprehend the dynamics of return volatility.
Researchers are increasingly focused on how major events and unexpected shocks influence return volatility in financial markets A crucial aspect of this analysis is the concept of persistence in variance, which indicates that past volatility can significantly impact current volatility levels Greater persistence means that historical volatility has a stronger explanatory power over current fluctuations Understanding this persistence is essential for predicting how events affect stock return volatility and ultimately influence stock prices According to Poterba and Summers (1986), the impact of stock-return volatility on prices, mediated by a time-varying risk premium, is heavily reliant on the permanence of shocks to variance Therefore, assessing the degree of persistence in conditional variance within daily stock-return data is a vital economic consideration.
ARCH models developed by Engle and Bollerslev (1982) and later generalized by Bollerslev (1986) and Taylor (1986) effectively capture time-varying stock return volatility and its persistence Research, including studies by Akgiray (1989) and Pagan et al (1989), supports the efficacy of GARCH models over non-GARCH alternatives for volatility estimation Since the inception of basic GARCH models, numerous extensions, such as GARCH in mean (GARCH-M) and Threshold GARCH (Glosten et al., 1993), have emerged to enhance the modeling of return series characteristics Additionally, the iterated cumulative sums of squares (ICSS) procedure introduced by Inclan and Tiao (1994) is widely utilized to identify significant changes in variance within time series, providing insights into the timing and magnitude of these shifts.
Despite limited research on Vietnam's stock market compared to mature and emerging markets, its rapid growth since the establishment of the Ho Chi Minh City Securities Trading Center (HOSTC) in 2000 is noteworthy Initially characterized by low liquidity and an incomplete legal framework, the market has evolved into a vital channel for capital mobilization and distribution, significantly contributing to the domestic economy By the end of 2010, the number of listed companies surged to 280, with a market capitalization of VND591 trillion, representing approximately 30% of Vietnam's GDP Additionally, foreign investors purchased over VND15 trillion in stocks, reflecting the market's attractiveness, as indicated by the VNIndex, a market-value-weighted index of HOSTC's common stocks.
This study aims to analyze and model stock return volatility in the Vietnam stock market using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH(p, q)) model The research employs GJG (TGARCH) and GARCH-in-mean (GARCH-M) models to explore leverage effects and risk-return premiums To identify significant sudden changes in variance, an iterated cumulative sums of squares (ICSS) procedure is applied, allowing for the estimation of time points and magnitudes of these changes The study also examines major events linked to increased volatility and discusses the relationship between volatility shifts in the Vietnam stock market and the global financial crisis in the US in 2008 These identified volatility regimes are incorporated into the standard GARCH model for further analysis.
"true" estimate of volatility persistence.
To solve the problem mentioned above, four research questions needed to be answered are:
Question 1 :What are characteristics of return volatility in Vietnam’s stock market? Are they similar to the results gained from previous researches?
Question 2 : Which volatility models are suitable to the stock return characteristics found out?
The ICSS algorithm identifies multiple break points or regime shifts, particularly during significant global economic crises Notable events corresponding to these regime shifts include the 2008 financial crisis and other pivotal economic downturns, highlighting the algorithm's effectiveness in detecting sudden changes in economic trends.
Question 4 :How do these regime shifts in stock return variance affect volatilities in models? And what is the change of persistence in variance after breakpoints are modified in models?
This thesis is organized into distinct sections rather than traditional chapters, as each topic does not warrant a separate chapter This structure aligns with the methodological guidelines set forth by Brooks (2008) The organization is as follows: Section 2 presents a brief literature review, Section 3 formulates the hypotheses, Section 4 delves into the econometric methodology of the selected models discussed in the literature review and applied in other countries, Section 5 reports the data and empirical results, and the final section provides a summary and concluding remarks.
LITERATURE REVIEW
Common characteristics of return series in the stock market
Numerous studies have highlighted key characteristics of financial time series, including volatility clustering, leptokurtosis, and asymmetry Volatility clustering suggests that significant price changes in financial markets tend to occur in groups, with large changes following large ones, and small changes following small ones Leptokurtosis indicates that stock return distributions are not normal, exhibiting fat tails and a higher likelihood of extreme values than predicted by normal distributions Asymmetry, or the leverage effect, describes how a decline in returns is typically followed by a more substantial increase in volatility compared to the volatility resulting from a rise in returns Research by Fama (1965) on daily stock prices of thirty Dow Jones Industrial Average stocks revealed evidence of return clustering and leptokurtosis in frequency distribution Similarly, Baillie and DeGennaro (1990) examined the US stock market from 1970 to 1987, noting high persistence and deviations from normal distribution characterized by leptokurtosis and negative skewness Poon and Taylor (1992) also explored the relationship between stock returns and volatility within the UK's Financial Times All Share Index during the same period.
The year 1989 marked a significant observation of clustering and high persistence in conditional volatility within the stock market These characteristics of stock return series have been consistently identified in subsequent research Notably, Emenike (2010) examined the volatility of stock market returns in the Nigerian Stock Exchange (NSE) from January 1985 to December 2008, uncovering similar features such as volatility clustering, leptokurtosis, and leverage effects, aligning with findings from earlier studies.
Volatility models suitable to the stock return characteristics
To analyze the volatility characteristics in financial time-series, various conditional volatility models have been developed, beginning with Engle's (1982) Auto-Regressive Conditional Heteroskedasticity (ARCH) model, which utilizes squared lagged disturbance values This was expanded by Bollerslev (1986) into the Generalized ARCH (GARCH) model, widely used for high-frequency financial data While both ARCH and GARCH effectively capture volatility clustering and leptokurtosis, they are limited by their symmetric distributions, which overlook the leverage effect To address this gap, several nonlinear GARCH extensions have been introduced, including the Exponential GARCH (EGARCH) by Nelson (1991) and the GJR-GARCH model by Glosten et al (1993) and Zakoian (1994) Additionally, Engle et al (1987) proposed the ARCH-M specification to explore the relationship between risk and return, leading to extensive research applications of these models.
Hamilton et al (1994) identified ARCH effects in US stock returns when analyzed at high frequencies, such as daily or weekly Bekaert and Harvey (1997) conducted an extensive study on the volatility of stock index returns across 20 emerging markets, including Argentina, Chile, and Taiwan, from January 1976 to December 1992, and found that modeling volatility was complex due to the unique behaviors of each country Additionally, F Lee, Chen et al (2001) applied GARCH and EGARCH models to daily returns of the Shanghai and Shenzhen index series, further contributing to the understanding of volatility in stock markets.
Between 1990 and 1997, studies revealed high persistence and predictability of stock return volatility, with no significant relationship found between expected returns and risks using the GARCH-M model Alberga, Shalit et al (2008) analyzed the Tel Aviv Stock Exchange (TASE) indices through various GARCH models, concluding that the asymmetric GARCH model with fat-tailed densities enhanced the estimation of conditional variance Similarly, Floros (2008) examined volatility in the Egyptian (CMA General index) and Israeli (TASE-100 index) markets from 1997 to 2007, employing several GARCH-type models, including EGARCH and TGARCH The findings indicated that these models effectively characterized daily returns, highlighting that risk and return fluctuations do not necessarily align.
Identification of breakpoints in volatilities and influence of the regime changes
In the context of stock market volatility, numerous studies focus on pinpointing the change points within sequences of independent random variables Research indicates that considering regime changes significantly diminishes the persistent ARCH/GARCH effects previously observed, as highlighted by Lamoureux and Latrapes.
In their seminal study, the authors (1990) examined the effects of jumps in unconditional variance within conditionally heteroscedastic time series by analyzing 30 exchange-traded stocks from January 1963 to November 1979 using the GARCH (1, 1) model They found that the standard GARCH model's parameters were overstated when regime shifts in variance were not accounted for Lacking a robust methodology, they divided the study periods into non-overlapping intervals to identify sudden variance changes A significant advancement was introduced by Inclan and Tiao (1994) through their iterative cumulative sums of squares (ICSS) algorithm, which effectively detects multiple breakpoints in variance across independent observations This approach revealed that financial time series typically exhibit stationary behavior interrupted by sudden changes in error term variability The ICSS algorithm, which reduces the computational burden of traditional methods, yielded results comparable to Bayesian and likelihood ratio tests Subsequent studies, including those by Aggarwal and Inclan (1999), confirmed the presence of volatility shifts in emerging markets, while Malik and Hassan (2004) and others demonstrated that incorporating breakpoints into the GARCH(1,1) model significantly reduced volatility persistence across various stock sectors and markets.
27, 2006; and Long (2008) for VNIndex in the Vietnam stock market from July
Events related to regime changes
Research indicates that high volatility in stock markets is often linked to significant local political, social, and economic events rather than global occurrences Aggarwal, Inclan et al (1999) found that critical political events frequently trigger sudden volatility shifts, with the October 1987 crash being a notable global event impacting emerging markets like Mexico, Singapore, and the US Their findings align with those of Bekaert and Harvey (1997), Susmel (1997), and Bailey and Chung (1995) Bacmann and Dubois (2002) further supported this by analyzing stock returns in several Asian and Latin American countries, concluding that volatility spikes were country-specific and could be mitigated through diversification Additionally, Long (2008) highlighted that regime changes in the Vietnam stock market often coincided with shifts in market mechanisms and political developments.
Research by Malik and Hassan (2004) analyzing five major Dow Jones stock indexes across various sectors from 1992 to 2003 revealed that most volatility breaks were linked to global events rather than sector-specific news Similarly, Hammoudeh and Li (2006) supported this perspective, indicating that significant global events were the primary influences on Gulf Arab stock markets.
Sudden changes in economic recession?
The impacts of crises on stock return volatility remain a significant concern for investors and researchers Fernandez (2006) examined the effects of the Asian crisis in Thailand in July 1997 and the September 11 attacks on global stock market volatility using the iterative cumulative sum of squares (ICSS) algorithm and wavelet-based variance analysis His analysis of eight Morgan Stanley Capital International (MSCI) stock indices revealed breakpoints around the Asian crisis, with Europe being notably affected after the 9/11 attacks Similarly, Wang and Moore (2009) utilized the ICSS algorithm to demonstrate that emerging stock markets, changes in exchange rate policies, and financial crises lead to abrupt volatility shifts These findings underscore the tangible impact of crises on stock markets, albeit at varying levels.
Overstatement of ICSS algorithm in raw returns series
The ICSS algorithm, widely utilized in various studies, has been criticized for overstating actual variance shifts due to its reliance on the assumption of independent time-series, which stock returns violate due to conditional heteroscedasticity Bacmann and Dubois (2002) addressed this issue by filtering return series through a GARCH (1,1) model, applying the ICSS algorithm to the standardized residuals, which helped mitigate serial correlation and ARCH effects Their findings, which revealed that variance jumps in stock market indices of ten emerging markets were less frequent than previously thought, contrasted significantly with earlier research by Aggarwal et al (1999) Subsequent studies, including Fernandez (2006) and Long (2008), supported Bacmann and Dubois's conclusions, noting a substantial decrease in detected shifts when using filtered returns This work aims to enhance the empirical literature on stock return volatility in the Vietnam stock market, extending the analysis to include the global economic crisis period to assess its impact on volatility patterns and the relationship between global recessions and the Vietnam stock market.
HYPOTHESES
Basing on the mentioned research questions and the above literature review, the hypotheses are formulated as follows:
Volatility characteristics of return series and corresponding models:
A literature review highlights that financial asset return series commonly exhibit features such as volatility pooling, high persistence, and non-normal distribution These characteristics are effectively modeled using GARCH, GARCH-M, and TGARCH frameworks Consequently, the following hypotheses are proposed.
Hypothesis 1: Return volatility in Vietnam stock market has similar characteristics as found in financial theory (Answer in Section 5.1 and 5.2.1.3)
Hypothesis 2: GARCH models are suitable to characterize volatility of Vietnam stock market’s return series (Answer in Section 5.2.1.3)
Breakpoint identification and influence of regime shifts on volatility persistence:
The ICSS algorithm, introduced by Inclan and Tiao in 1994, is widely utilized for detecting sudden jumps in return variance, as evidenced by studies from Aggarwal et al (1999), Malik et al (2005), and Long (2008) Research indicates that events leading to volatility changes can be either local or global, varying by country-specific contexts While some stock markets exhibit breakpoints during crisis periods, others do not Notably, incorporating regime shifts into the standard GARCH model has been shown to reduce variance persistence Consequently, two hypotheses are proposed for the Vietnam stock market.
Hypothesis 3: Many breakpoints (including in economic crisis period) are found by ICSS algorithm in research periods All sudden changes are corresponding to remarkable events.(Answer in Section 5.2.2.1 and 5.2.2.2)
Hypothesis 4: These regime shifts in stock return variance strongly affect volatilities and reduce persistence in variance in modified models (Answer in
RESEARCH METHODS
Stationarity
A stationary series is characterized by a constant mean, constant variance, and consistent autocovariances for each lag, as defined by Brooks (2008) Determining whether a series is stationary is crucial for various analytical purposes.
The stationarity of a time series significantly affects its behavior and characteristics A 'shock' refers to an unexpected change in a variable or the error term during a specific time period In a stationary series, these shocks diminish over time; for instance, the impact of a shock at time t decreases in time t+1 and continues to lessen in subsequent periods.
Using non-stationary data in regression analysis can result in spurious regressions, where standard techniques yield seemingly significant coefficient estimates and a high R² value However, these results can be misleading and ultimately lack real value, leading to the classification of the model as a 'spurious regression.'
According to Gujarati (2003), the analysis of a non-stationary time series is limited to the specific time frame of the study, making it impossible to generalize findings to other periods For effective forecasting, non-stationary series lack reliability, as they assume that past and present volatility trends will continue into the future Consequently, if the data is subject to frequent changes, accurate future predictions cannot be made Thus, the fundamental requirement for reliable time series forecasting is that the series must be stationary.
Testing for stationarity
Two popular methods for testing stationarity are autocorrelation diagram and unit root test.
Autocorrelation measures the relationship between the current stock return and its value in the previous period It is calculated as:
The serial correlation coefficient of stock returns at lag k, denoted as pk, is calculated using the number of observations, N It assesses the relationship between stock returns at time t, represented as rt, and stock returns at a future time t+k, denoted as rt+k Additionally, r represents the sample mean of the stock returns, while k indicates the lag period.
The autocorrelation function (ACF) is used to assess the presence of serial correlation in data The primary goal of the autocorrelation test is to evaluate whether the serial-correlation coefficients significantly differ from zero This analysis involves testing two hypotheses.
In a random time series, the autocorrelation coefficients behave as random variables that follow a normal distribution with a mean of 0 and a variance of 1/N By utilizing the standard error of the autocorrelation coefficient, which is 1/N, we can establish a confidence interval for pk If the value of pk falls outside this confidence interval, the null hypothesis can be rejected.
The Ljung-Box portmanteau statistic (Q) is utilized to assess the joint hypothesis that all autocorrelations are equal to zero In the autocorrelation plot, the last two columns display the Ljung-Box Q-statistics alongside their corresponding probabilities The calculation of the Ljung-Box Q-statistics is essential for this analysis.
The Q-statistic is utilized to test the null hypothesis of zero autocorrelation in the first k autocorrelations, represented as p1 = p2 = p3 = = pk = 0 Under this hypothesis, the Q-statistic follows a chi-squared distribution, with degrees of freedom corresponding to the number of autocorrelations (k) being analyzed.
The unit root test is a widely used method for determining the stationarity of a time series Pioneering research by Dickey and Fuller in the 1970s laid the groundwork for this testing approach The primary aim of the unit root test is to evaluate the null hypothesis that the parameter φ equals 1, as expressed in the equation yt = φyt-1 + ut, where -1 ≤ φ ≤ 1 The test specifically examines this hypothesis against the one-sided alternative that φ is less than 1.
In practice, the following regression is employed, rather than (4.1), for ease of computation and interpretation t t t y u y
1 (4.2) so that a test of = 1 is equivalent to a test of = 0 (since − 1 = ) And the above hypotheses become:
Dickey-Fuller (DF) tests, also referred to as τ-tests, can be performed with various configurations, including an intercept, an intercept with a deterministic trend, or without any of these elements in the regression In each scenario, the null hypothesis of a unit root is rejected in favor of a stationary alternative if the test statistic is more negative than the critical value.
GARCH model
There are two equations estimated in a basic model, one for the mean which is a simple ARMA model and another for the variance which is identified by a particular ARCH specification.
Time series models aim to empirically capture significant characteristics of observed data, which may stem from various unspecified structural models A key type of time series model is the AutoRegressive Integrated Moving Average (ARIMA) model, initially introduced by Box and Jenkins in 1976.
The simplest class of time series model that one could entertain is that of the moving average process Letu t (t= 1, 2, 3, .) be a white noise process with E(u t )
= 0 and var(u t ) = 2 Then q t q t t t t u u u u y 1 1 2 2 is a q th order moving average mode, denoted MA(q) This can be shortly expressed as
A moving average model is a linear combination of white noise processes, where the value of \( y_t \) relies on both current and past white noise disturbances This means that the current value of \( y \) at time \( t \) is influenced by both present and historical information, with recent news holding greater significance than older data.
To identify the q-th lag in time series analysis, we utilize the autocorrelation plot The autocorrelation function (ACF) displays a significant non-zero trend that becomes zero after the q-th lag, while the partial autocorrelation function (PACF) shows an immediate zero trend.
The partial autocorrelation function (PACF) quantifies the relationship between a current observation and an observation from k periods prior, while accounting for the influence of intermediate observations Specifically, it assesses the correlation between yt and yt−k by eliminating the effects of the intervening values y t−k+1, y t−k+2, , y t−1.
An autoregressive model is one where the current value of a variable, y, depends upon only the values that the variable took in previous periods plus an error term.
An autoregressive model of orderp, denoted as AR(p), can be expressed as t p t p t t t y y y u y 1 1 2 2 where u t is a white noise disturbance term and presents average value of the series.
This expression can be written more compactly using sigma notation as below:
Autoregressive models are ideally suited for stationary time series, as stationarity is a key characteristic that enhances the reliability of AR model estimates A significant concern with non-stationary coefficients is that they can lead to persistent influences of past error terms on the current value of the dependent variable, y t, over time.
1 is the important condition to ensure stationarity of the series y t
In the context of MA(q) models, the p-th lag can be identified using an autocorrelation plot The autocorrelation function (ACF) shows a zero trend right away, while the partial autocorrelation function (PACF) exhibits a significant non-zero trend up to the p-th lag, after which it drops to zero.
Many time series do not meet the criteria for AR(p) or MA(q) models individually; however, they frequently combine both approaches This indicates that a stationary time series can be represented as an ARMA(p, q) model.
An ARMA(p, q) model integrates the features of both AR(p) and MA(q) models, making it suitable for stationary time series data This model expresses the current value of a series, denoted as y, as a linear function of its past values along with a mix of current and past values from a white noise error term.
The following is the summary of the characteristics defining AR, MA and ARMA processes:
a number of non-zero points of pacf = AR order.
a number of non-zero points of acf = MA order
A combination autoregressive moving average process has:
4.3.1.4 Information criteria for ARMA model selection
In the identification stage of time series analysis, relying on graphical plots of the autocorrelation function (ACF) and partial autocorrelation function (PACF) is often ineffective due to the complexity of real data, which rarely shows clear patterns This complexity makes it challenging to accurately interpret these plots and select a suitable model To mitigate the subjectivity associated with ACF and PACF interpretation, analysts can utilize information criteria, providing a more objective approach to model specification.
The two most widely used information criteria for analyzing time series models, such as ARIMA, ARCH, and GARCH, are Akaike's Information Criterion (AIC) introduced by Akaike in 1974 and the Schwarz Bayesian Information Criterion (SBIC) proposed by Schwarz in 1978.
The SBIC formula is represented as SBIC = σ² + k, where σ² denotes the residual variance, calculated as the residual sum of squares divided by the sample size T In this equation, k refers to the total number of estimated parameters, and T indicates the sample size utilized in the analysis.
When selecting a model, it is advisable to choose one that minimizes the value of an information criterion However, it's important to note that different criteria can yield conflicting results, leading to varied conclusions Therefore, the general principle is to opt for a model that consistently demonstrates lower values across multiple criteria.
While linear estimators are extensively studied and understood, many financial relationships are inherently non-linear Key characteristics of financial data, such as leptokurtosis, volatility clustering, and leverage effects, cannot be adequately captured by linear models Various non-linear models have been developed, with the Autoregressive Conditionally Heteroscedastic (ARCH) and Generalized ARCH (GARCH) models being among the most widely used for modeling and forecasting volatility in finance.
Engle (1982) introduced ARCH processes to model time-varying conditional variance by utilizing lagged disturbances, effectively capturing key characteristics of economic and financial data These models account for thick-tailed unconditional distributions and the phenomenon of volatility clustering, where variances fluctuate over time regardless of their sign In the ARCH framework, the autocorrelation in volatility is represented by making the conditional variance of the error term, σ²ₜ, dependent on the preceding squared error value.
(4.5) where u t : is error term at time t t 2
: conditional variance for the current time t
2 j u t : news about volatility from the previous period, measured as the lags of the squared residual from equation (4.3)
The ARCH model comprises a conditional mean equation and a conditional variance equation Researchers have the flexibility to specify the form of the conditional mean equation as desired It is essential that all coefficients in the model are non-negative, ensuring that each coefficient meets the requirement of being greater than or equal to zero.
The above formulations known as a full model of an ARCH(q) model where the error variance depends onqlags of squared errors.
The advantage of ARCH formulation is that the parameters can be estimated from historical data and used to forecast future patterns in volatility.
TGARCH Model
GARCH models traditionally enforce a symmetric response of volatility to both positive and negative shocks However, research suggests that negative shocks may increase volatility more significantly than positive shocks of equal magnitude To address this asymmetry, various nonlinear extensions of GARCH have been introduced, notably the GJR model, also known as Threshold GARCH or TGARCH, developed by Zakoian (1994) and Glosten, Jagannathan et al (1993) The GJR model enhances the GARCH framework by incorporating an additional term to capture potential asymmetries in volatility response.
= 0 otherwise For a leverage effect, we would see > 0 Notice now that the condition for non- negativity will be > 0, 1 > 0,β ≥ 0, and 1 + ≥ 0.That is, the model is still admissible, even ifγ 0 then the leverage effect exists between bad news and good news, while if
In financial models, investors are typically compensated for assuming greater risk with the potential for higher returns This principle is implemented by linking the return on a security to its associated risk levels, as discussed by Engle, Lilien, and others.
In 1987, an ARCH-M model was proposed that integrates the conditional variance of asset returns into the conditional mean equation Today, GARCH models have gained significant popularity over ARCH models, leading to a more frequent estimation of GARCH-M models The GARCH-M model is defined by a specific mathematical specification that reflects this relationship.
A positive and statistically significant δ indicates that an increase in conditional variance, which represents heightened risk, corresponds to a rise in mean return Consequently, δ can be understood as a risk premium In various empirical applications, this relationship is often expressed in a square root form.
t , appears directly in the conditional mean equation, rather than in conditional variance term, t 2 Also, in some applications the term is lagged rather than contemporaneous, t 2
The ICSS algorithm, developed by Inclan and Tiao in 1994, is designed to identify sudden shifts in variance resulting from shocks in time series data In this context, the time series ε t is characterized by a zero mean and an unconditional variance σ 2 t, exhibiting stationary variance during initial periods until a sudden break occurs Following each break, the variance remains stationary until the next abrupt change, creating a sequence of observations with multiple breakpoints in the unconditional variance across T observations Each interval's variance is denoted as τ j, where j ranges from 0 to NT, and the breakpoints are represented by the ordered set 1 < κ 1 < κ 2 < < κ NT.
To estimate the number of changes in variance and the time points of each variance shift, Ckwhich presents cumulative sum of squares is used Ckis calculated as
2, k= 1, 2, …, T Then, theD k statistic is defined as below:
Inclan and Tiao (1994) demonstrated that the D k plot remains centered around zero for series exhibiting homogeneous variance However, in the presence of a sudden change or break point, the D k plot surpasses predetermined boundaries, showing significant upper and lower variance fluctuations A change point is indicated when the maximum absolute value of D k exceeds the critical threshold.
In this analysis, we define k* as the moment when the maximum absolute value of D k is observed If the maximum of the standardized distribution of D k at k* exceeds the established thresholds, k* serves as an estimate for the change point According to Inclan and Tiao (1994), the critical value of 1.358 represents the 95th percentile of the asymptotic distribution of max standardized D k, allowing us to set upper and lower boundaries at +/- 1.358.
Inclan and Tiao (1994) raised concerns about the reliability of the D k function for identifying multiple break points simultaneously due to the potential "masking effect." They recommend an iterative approach that applies the D k function successively to segments of the series, starting with the entire dataset to determine the first break point (k1*) Each resulting sub-series is then analyzed with the D k function, continuing this process until the maximum standardized D k falls below the critical threshold of 1.358 Once all break points are identified, a final verification step is conducted to assess the existence and convergence of these points by applying the D k function across each phase, ensuring that the newly identified points are consistent with those found in previous iterations.
Inclan and Tiao (1994) suggest that the ICSS algorithm serves as a valuable tool for residual diagnostics in time series modeling Simulation results indicate that applying the ICSS algorithm to the residuals of autoregressive processes yields results comparable to those derived from independent observation sequences.
4.7 Combination of GARCH model and sudden changes
Research by Lamoureux and Latrapes (1990) highlights that the application of standard GARCH models can lead to an overestimation of volatility persistence, especially in series characterized by sudden variance changes To achieve reliable parameter estimates in the conditional variance equation, it is essential to incorporate regime shifts into the standard GARCH model Therefore, after identifying the break points responsible for these abrupt changes, the ARCH/GARCH model should be modified accordingly.
D 1 , D 2 , , D n are a set of dummy variables controlling for regime changes, taking a value of one from each point of sudden change of variance onwards, and zero elsewhere.
is the constant term that stands for the average volatility of the first volatility regime, ignoring any effect of past residuals on the conditional variance.
The coefficients of D 1 , D 2 , , D n show how the subsequent regimes’ volatility is different from the first regime volatility and how the volatility varies between different regimes.
Data
This study utilizes a dataset of 2,121 daily closing stock price observations from the Hochiminh Stock Exchange (www.hsx.vn), covering the period from March 1, 2002, to August 31, 2010 This timeframe represents the most current data available at the time of the research, and March 1, 2002, was selected to ensure consistency in the analysis, as securities trading has been conducted daily since then The VNIndex of the Hochiminh Stock Exchange, which has a nearly four-year longer history than the Hanoi Stock Exchange, is chosen to represent the Vietnam stock market index, as it is a capitalization-weighted index encompassing all companies listed on Vietnam's official stock exchange.
Table 5.1 shows the descriptive statistics for daily stock market returns with daily returns computed as below:
Rt= ln(Pt/ Pt-1) where Ptis the daily price at timetand Pt-1is the daily price at timet-1.
Table 5.1 Descriptive statistics of Vietnam stock market’s daily return series
Statistics reveal that daily average returns are positive yet minimal in comparison to the standard deviation Literature frequently highlights that daily return series deviate from normality, notably exhibiting excess kurtosis and asymmetry The positive skewness coefficient of 0.014 suggests a rightward skew in the data Additionally, the Vietnam stock market's return kurtosis is 4.14, indicating a leptokurtic distribution characterized by fatter tails and a sharper peak at the mean compared to a normal distribution.
The Jarque-Bera statistic, with a value of 115.73, indicates that the returns of the Vietnam stock market do not follow a normal distribution, supporting the hypothesis of non-normality and highlighting the presence of excess kurtosis.
The conclusion that daily return series observed in Vietnam stock market have non- normality distribution is reasonable, as it is common phenomenon in emerging markets’ data set.
The autocorrelation and stationarity of the Vietnam stock market's returns were analyzed using the Ljung-Box (LB) and Augmented Dickey-Fuller (ADF) test statistics, with findings detailed in Tables A2, A3 in the Appendix, and Table 5.2 Notably, Table A2 indicates a significant autocorrelation in stock returns.
Table 5.2 Unit Root Test on VNIndex’s daily return
Null Hypothesis: R has a unit root
Lag Length: 3 (Automatic based on SIC, MAXLAG%) t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -18.95251 0.0000
The Augmented Dickey-Fuller (ADF) test indicates that the stock return series is stationary, as evidenced by the test statistic's larger absolute value compared to the critical value at the 1% significance level.
The presence of autocorrelation and stationarity indicates significant volatility clustering, suggesting that the volatility trends of past and present values can offer insights into future returns Figure 5.1 illustrates the volatility clustering observed in daily stock returns.
Figure 5.1 Daily return series on HOSE
In summary, volatility features of return series are similar to the studies of Fama
(1965), Baillie and DeGennaro (1990), Poon and Taylor (1992) and recentlyEmenike (2010).
Empirical results
5.2.1 Suitable models for stock return series of Vietnam
A basic GARCH model involves estimating two equations: one for the mean and another for the variance Given the characteristics of the data and the stationarity of the time series, ARMA models are likely appropriate for the mean equation in this context.
In the analysis of various ARMA models, four models emerged as statistically significant, demonstrating a dependence of returns on their previous values and the current and past error terms These models are ARMA(1,0), ARMA(2,0), ARMA(0,1), and ARMA(1,2) The regression results indicate that the coefficients for all equations are statistically significant at the 1 percent level, with the exception of the constant term C Consequently, models that do not include a constant C appear to be more suitable for this analysis.
Table 5.3 Empirical results of different ARMA models
The ARMA(1,2) model, which exhibits the lowest values for both the Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (SBIC), is identified as the most appropriate model for analyzing stock return series in the Vietnam stock market.
Before estimating a GARCH-type model, it is crucial to test for the presence of ARCH effects to ensure the model's suitability for the data The Eviews estimation results indicate significant ARCH effects up to the 7th lag, as shown in Table 5.4 This finding aligns with the high-frequency stock return series in the Vietnam stock market and is consistent with the research conducted by Hamilton, Susmel, et al (1994).
Table 5.4 ARCH effect at 7 th lag
Obs*R-squared 387.4714 Prob Chi-Square(7) 0.0000
Coefficient Std Error t-Statistic Prob.
S.E of regression 0.000419 Akaike info criterion -12.71396
Sum squared resid 0.000369 Schwarz criterion -12.69254
Log likelihood 13433.94 Hannan-Quinn criter -12.70612
A parsimonious GARCH(p,q) model is preferred over an ARCH model with excessive lags for result estimation, as it permits an infinite number of past squared errors to influence conditional variance In the subsequent analysis, various GARCH-family models are estimated using an ARMA(1,2) mean equation to effectively capture the characteristics of stock return series.
Table 5.5 presents the parameter estimates for all statistically significant GARCH-family models applied to the return series of the Vietnam stock market.
Table 5.5 Empirical results of different GARCH-family models
• We report the results from GARCH-type models using the method of maximum likelihood, under the assumption that the errors are conditionally normally distributed
GARCH models, specifically GARCH(1,1), GARCH(2,1), and GARCH(3,1), demonstrate statistically significant parameters at the 10% level, highlighting the presence of strong GARCH effects These models indicate that the variance at time t is influenced by previous observed shocks.
2 ) and the past value of itself in the last periods (
) GARCH (2, 1) with the smallest AIC and SBC seem to be the most suitable model.
The coefficients of all models concerning lagged squared error and lagged conditional variance sum to nearly one, indicating that shocks to conditional variance exhibit significant persistence This suggests that current volatility levels are positively correlated with those from previous periods, aligning with the findings of researchers such as F Lee, Chen et al (2001) and Floros (2008).
GARCH-M Models: With non-negative conditions for all parameters, only
The GARCH-M (1, 1) and GARCH-M (2, 1) models demonstrate statistical significance, with positive and significant coefficients (δ) for conditional variance in the mean equation at the 10% level This indicates that investors who assume higher risks are rewarded with greater returns Based on the selection criteria for GARCH models, GARCH-M (1, 1) is deemed more suitable These results contrast with findings from studies by Floros (2008) on the Egyptian and Israeli markets, as well as F Lee, Chen et al (2001) concerning four Chinese stock exchanges.
The TGARCH model reveals a positive asymmetric coefficient of 0.038, which is not statistically significant at the 10% level, indicating that there is no discernible difference in the impact of good versus bad news on stock returns Consequently, the response of volatility to both positive and negative shocks is symmetric, contrasting with the volatility trends observed in TASE indices in Israel, as noted by Alberga, Shalit et al.
(2008) and of CMA General index in Egypt by Floros (2008).
In summary, GARCH family is suitable to characterize return volatility of Vietnam stock market and such strong volatility in Vietnam stock market is compensated by high-risk premium.
5.2.2 Identification of break points and detection of related events
This section will identify and compare breakpoints in both raw and filtered return series, highlighting the exaggerated results of the ICSS method when applied to raw data Additionally, we will analyze events associated with abrupt changes in the filtered data.
Using ICSS algorithm for raw returns series, total 23 breakpoints are found and presented in Table 5.6
Table 5.6 Breakpoints detected by ICSS algorithm in the raw returns
No Time period Duration Events
29/07/2002 5 months - March 1, 2002: increase in number of transaction sessions from 3 to 5 sessions per week
26/02/2003 7 months - August 1, 2002: broadening transaction band from 2% to 3%
- December 22, 2002: adjustment of stock price transaction band up to 5% from 3%
29/04/2003 26 days - April 2003: boom of interest rate race
03/12/2003 7 months - August 2003: promulgation of Decision No 146/2003/QĐ-
TTg allowing foreign investors to buy up to 30 percent of stock value of a privatized enterprise.
On November 28, 2003, Decree No 144/CP was enacted to supersede Decision No 48/CP, introducing new measures aimed at enhancing the environment for stock issuance and trading This decree focuses on ensuring a safe, public, transparent, and efficient operation of the stock market.
19/02/2004 2 months - January 4, 2004: set up of Vietnam Association of Financial
Investor (VAFI) creating general voice among enterprises, securities companies and investors with authorities
- February 19, 2004: Decree No 66/2004/NĐ-CP of the Government to shift State Securities Commission of Vietnam (SSC) to Ministry of Finance
26/05/2004 > 1.5 months - May 14, 2004: foundation of Vietnam Association of
07/01/2005 3 months - November 8, 2004: Vietnam Securities Investment Fund
- November 16, 2004: issuance of Decree No 187/2004/NĐ-
CP to replace Decree 64/2002/NĐ-CP about equitization of state-owned enterprises
25/03/2005 > 2 months - March 8, 2005: the establishment of Hanoi Securities Trading
16/09/2005 4 months - June 14, 2005: approval of Decision No 528/QĐ-TTg from
Prime Minister on the list of equitised enterprises, which auction shares, list and register for transactions at Vietnam’s securities exchange centers
- July 27, 2005: Decision No 189/2005/QĐ-TTg on establishment of Vietnam Securities Depository (VSD)
- August 16, 2005: a club of listed companies set up
08/11/2005 > 1.5 months - September 29, 2005: Decision No 238/2005/QĐ-TTg by the
Prime Minister on percentage of participant of foreign parties in securities market of Vietnam
- November 1, 2005: Decision No 491/ QĐ-UBCK by Chairman of State Securities Commission on promulgating Formal Statue of auctioning in Securities Trading Center.
31/08/2010 > 4 years - June 29, 2006: the promulgation of the Law of Securities with validity from January 1, 2007
- September 8, 2006: Official Dispatch No 10997/CV-BTC of Ministry of Finance released
- May 28, 2007: issuance of Directive No 03/2007/CT-NHNN of the State Bank of Vietnam to curb inflation
- July 30, 2007: continuous order matching officially applied by HOSE
- August 8, 2007: HCM City Securities Trading Center (HOSTC) renamed to HCM City Stock Exchange (HOSE)
- February 1, 2008: Decision No 03/2008/QD-NHNN on lending, discount of valuable papers for securities investment and trading (of which lending limit on total chartered capital was not over 20%)
- Early of March 2008: SCIC declared to buy “good, efficient and highly liquid” shares to prevent downward trend in Vietnam stock market
- March 27, 2008: adjustment of daily trading band of HOSE to 1% from 5%
- April 7, 2008: : increase of daily trading band on HOSE to
- June 19, 2008: broadening daily trading band of HOSE to 3%
- August 18, 2008: recovery of HOSE’s daily trading band to 5%
- January 12, 2009: officially applying online transaction on HOSE
- February 10, 2009: Decree No 14/2007/NĐ-CP on transferring companies with chartered capital below VND80 billion to HNX
- June 1, 2009: Decision No 55/209/QĐ – TTG of the Prime Minister on allowing foreign investors to own up to 49% of shares of listed companies (replacing Decision No.
- July 6, 2009: reducing credit growth target to 25% - 27% (instead of 30%) to curb inflation
- August 22, 2009: increasing credit growth target to 30%
- January 1, 2010: application of Personal income tax on stocks’ trading and investment
- May 2010: promulgation of Circular No 13/2010/NHNN that became valid on October 1, 2010 The circular regulated the credit institutions on prudential ratios.
The analysis of breakpoints using raw returns reveals that, apart from a single instance lasting over four years, most shifts occur over relatively short durations, with some lasting only a few days and the longest spanning just seven months Such brief periods may not adequately capture market volatility responses to events or identify trends Additionally, many shifts appear unrelated to significant information that could impact stock market volatility, suggesting potential information lag or leakage Notably, no breakpoints were observed in the Vietnam stock market during the global economic crisis, contrasting with findings from previous studies by Fernandez (2006) and Wang and Moore (2009).
To visualize the breakpoints mentioned above in stock returns, a plot of sudden changes in variance combination with fluctuation in stock return is presented below:
Figure 5.2 Structural breakpoints in volatility in raw returns
Note: Bands at +/- 3 standard deviation, breakpoints estimated by using the ICSS algorithm
The return series is illustrated with +/- 3 standard deviations, highlighting volatility breakpoints marked by discontinuities in the lines Notable spikes in market return volatility were observed in early 2004 and between early 2006 and August 2010, aligning with an upward trend in stock price volatility in the Vietnamese stock market during these times.
Research has shown that the GARCH (1,1) model effectively captures the volatility of financial time series, as demonstrated by Hsieh (1989), who highlighted its ability to account for stochastic dependencies Subsequent work by Bollerslev, Chou et al (1992) reviewed extensions of ARCH models and empirical applications, concluding that GARCH (1,1) is adequate for most financial scenarios without necessitating more complex models This perspective is further supported by Taylor (1994) and Brooks and Burke, reinforcing the model's robustness in financial analysis.