19 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
The Empirical Study of Volatility Asymmetry
for FinTech ETF
Jo-Hui Chen and Chia-Shan Tung
Chung Yuan Christian University, Taiwan, R.O.C.
Abstract This study explores the price asymmetry of Financial Technology (FinTech),
Financial, and Technology ETFs data by using the Exponential Generalized Autoregressive
Conditions Heteroscedastic (EGARCH), Glosten, Jagannathan and Runkle (GJR-GARCH) and
the Jump model to measure the price volatility asymmetry accurately. This paper confirms that
the Autoregressive Moving Average- Generalized Autoregressive Conditions Heteroscedastic
(ARMA-GARCH) can eliminate the ARCH's residuals. The empirical results revealed that each
group of ETFs has price fluctuation asymmetry in the EGARCH model, meaning that the
impact of bad news is greater than good news. In the GJR-GARCH model, the results confirmed
that the Financial ETF has price asymmetry, and the bad news received for different volatility
will be greater than the good news. Finally, in the jump model, the Technology ETF is found
to have the most discrete effect.
Key words: FinTech ETF, ARMA-GARCH, EGARCH, GJR-GARCH, Jump, Asymmetry
20
1. Introduction
Recently, there has been a popular word in the financial world—FinTech (Financial
Technology), which is to introduce some related to the financial industry into technology. It
can also be interpreted as providing relevant technology services to the financial community,
and these services have long been related to our lives. Payments connected with investment,
wealth management, insurance, loans, and ordinary personal consumption payments are
familiar to the general public. Due to continuous innovation in technology, it has brought many
new startups. Funding inflows will be made to Angel Investor, Venture Capital (VC), private
equity, and Initial Public Offerings (IPO) proposals.
McAuley (2015) defined FinTech a financial industry composed of companies that used
technology to make financial systems more efficient1. FinTech companies cover industries such
as crowdfunding, peer-to-peer lending, algorithmic asset management, and thematic investing.
FinTech companies also operated in payments, data collection, credit scoring, education
lending, digital currency, exchanges, working capital management, cybersecurity, and even
quantum computing.
In the early 1990s, the lower cost of financial transactions affected by the internet
revolution has turned the traditional financial industry into electronic finance (e-finance),
including online banking, online brokerage services, mobile payments, and mobile banking.
After the financial crisis of 2008, new FinTech companies emerged and combined with artificial
intelligence, e-finance, internet technology, social media, social networking services, and big
data analytics. To get rid of the financial impression, these startups begin to change the financial
world, and let Financial and Technology to cooperate. The global FinTech boom began in 2015,
and many new types of corporate companies started to emerge. FinTech companies reflected
the performance of the Global index. For example, STOXX Global FinTech index, Selective
FinTech index, Nasdaq KFTX FinTech index and CedarIBS FinTech Index (CIFTI), etc.
It is observed that more and more funds are invested in the FinTech industry. In 2016, the
first pure FinTech ETF was officially born. In 2018, the private investment in the global
FinTech field exceeded 100 billion US dollars for the first time. Meanwhile, the rate of return
reached 18.86%2, becoming a financial product with a strong performance in the US stock
market. It has also become a project of concern to investors, and it has also made investors pay
more attention to the forecast of FinTech ETF price fluctuations.
Among them, Alberg, Shalit, and Yosef (2008) and Li (2007) used EGARCH to estimate
stock market volatility and revealed that the EGARCH model has a reasonable estimate of stock
market volatility. Some scholars also applied EGARCH in ETF finance. For example, Chen
and Huang (2010) and Chen and Diaz (2012) utilized EGARCH-ARMA to find in different
markets or strategies. ETFs are fluctuating asymmetry related to a leverage effect, meaning that
they can be affected by market news.
1 McAuley, Daniel (2015). What is FinTech? Source: www.medium.com/wharton-fintech/what-is-fintech-
77d3d5a3e677 2 CMoney Report (2019). Source: www.cmoney.tw/notes/note-detail.aspx?nid=166310.
21 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
In addition to using EGARCH for analyzing asymmetry and leverage effects, Duan and
Lin (2014) explored the implied volatility model and the ability of the intraday earnings
volatility model to predict ETF return volatility. Ou and Wang (2010) used EGARCH and GJR-
GARCH models to predict the financial volatility market of the three major ASEAN stocks and
found that forecasting volatility has a leverage effect. Their findings reveal the impact of price
fluctuations on the news.
Both Sim and Zurbreugg (1999) and Chang (2002) used various GARCH models to
explore the asset-reward hypothesis, which is subject to continuous diffusion stochastic
processes. Boudt and Petitjean (2014) used the Dow Jones Industrial Average to judge the
impact of price jumps on the news. It was found that the news was significant, which caused a
significant increase in price jumps. Li, Zhang, Liu, and Zhang (2019) analyzed the liquidity risk
model for asset price dynamics when using jump and liquidity risk for discrete barrier option
pricing model. Their empirical results supported the concept of liquidity risk and jump effect
into potential asset price dynamics. However, Bates (1996) and Das and Sundaram (1999)
revealed that the characteristics of the discrete jump would not cause the price deviation
problem.
Many documents in the past EGARCH, GJR, and jump models explored the asymmetry
in the stock market and the foreign exchange market, but the relevant industries have not yet
studied in the ETF literature. This research hopes to formulate investment strategies in
emerging industries, and then joins the financial and technology industries for analyzing more
comparable to price fluctuations in related industries. Thus, the purposes of this study are to
determine the asymmetry of volatility using EGARCH and GJR models connected with a
leverage effect. When the effect appears that the bad news on the market is greater than the
good news, and the GJR model adds more close confinement to make the leverage effect more
accurately. Moreover, this paper also examines the jump model, which can more accurately
detect fluctuations in events under asymmetric fluctuations. Symmetric models like ARCH and
GARCH, asymmetric GARCH can measure more accurately determine price asymmetry,
providing future investors with a strategic reference to enter the industry.
The second section focuses on the sources of FinTech, the relevant literature of ETFs, and
the empirical discussion of GARCH models. The third section introduces the source of
information and the GARCH family, and the fourth section conducts empirical research. The
fifth section gives the conclusion.
2. Literature Review
This study examined the literature of FinTech to explore studies conducted by scholars in
the past. It also introduces the research and discussion of past ETFs in academia, and finally
discusses the application of models.
In the past literature, there were many predictive volatilities asymmetric GARCH models.
Leeces (2007) utilized the rolling regression parameters of three asymmetric volatility models
to estimate the fluctuations in Indonesian stock returns during the Asian crisis. It was found that
the precise adjustment mode is sensitive to model selection and asymmetric reaction modes.
Estimates of the smooth transition volatility model indicated the asymmetry of symbols and
22 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
sizes during the crisis. It can be said that the GACRH model can accurately determine the
volatility, and can examine the good or bad of the message. Yang and Doong (2004) used the
Multivariate GARCH (MGARCH) model to explore the asymmetric volatility of spillover
effect connected with the nature of the volatility transfer mechanism. It turns out that changes
in stock prices will affect future exchange rates. However, exchange rate changes have a less
direct impact on future stock price changes. GARCH has used the leverage effect of EGARCH,
GJR-GARCH, and the Autoregressive Fractionally Integrated Moving Average - Fractional
Integrated Asymmetric Power ARCH (ARFIMA-FIAPARCH) asymmetry in the past literature
to judge the quality of the message.
Using the EGARCH model, Gokcan (2000) used linear and nonlinear GARCH models to
predict volatility in emerging stock markets. It is found that the performance of the GARCH
model is better than the EGARCH model of the emerging stock market. Koutmos and Booth
(1995) used the EGARCH model for examining good news on price and volatility in the New
York, Tokyo, and London stock markets (market progress) and bad news (market decline). The
results showed that the news of the last market transaction was not good. The volatility spillover
effects of specific markets were more pronounced. In, Kim, Yoon, and Viney (2001) used the
of Vector Autoregressive (VAR)-EGARCH model to explore whether the Asian crisis is the
dynamic interdependence and the fluctuation transfer of Asian stock markets. They found that
Asian stock markets responded to local news and news from other markets, especially bad news.
Darrat, Rahman, and Zhong (2002) used the 5-minute intraday data to study the trading volume
and return volatility of the Dow Jones Industrial Average. They used EGARCH to measure the
volatility of earnings and found that most of the Dow Jones Industrial Average did not show a
correlation between trading volume and volatility. According to the order information arrival
hypothesis, there is a significant lead-lag relationship between the two variables in a large
number of Dow Jones industrial average stocks.
When applied to foreign exchange volatility, Yang (2006) revealed that the
semiparametric volatility model was superior to the GJR-GARCH model in terms of fitness.
Wang (2009) applied the hybrid asymmetric volatility method combined with the artificial
neural network (ANN) option pricing model to predict the price of derivative securities. The
results showed that the volatility of Gray-GJR-GARCH was higher than other methods in the
ANN option pricing model. It was found that GJR-GARCH can be applied to the asymmetric
effect. However, the EGARCH and GJR-GARCH models in the asymmetric model are most
perform well. McAleer (2014) studied the asymmetry and leverage effects in the conditional
volatility model and used GARCH, GJR, and EGARCH model. Among them, the GJR model
has appropriate regularity conditions.
In 2016, the ETF market won stocks in both volume and value. Wigglesworth (2017)
reported that “seven of the top 10 most actively traded securities in the US stock market are
ETFs, not stocks”3. In the era of ETFs, many scholars conducted not only spillover effect,
leverage effect, and long memory, but also different industries (i.e., oil, gold, and energy).
3 Wigglesworth, Robin. (2017). ETFs are Eating the US Stock Market. Financial Times. Source:
www.ft.com/content/6dabad28-e19c-11e6-9645-c9357a75844a.
23 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
In the past spillovers literature, Chen, Diaz, and Chen (2014) used moving averages
(ARMA) and seasonal autoregressive moving averages (SARMA) models to analyze seasonal
and spillover effects for real estate investments. There was a strong positive correlation between
the impact of bilateral returns and the Real Estate Investments Trusts (REIT) ETF and the
tracking index. Many scholars also analyzed the spillover effect and the leverage effect. Chen
and Huang (2010), Chen (2011), Chen and Diaz (2012), Chen and Maya (2014), and Chen and
Trang (2018) applied the EGARCH-ARMA and EGARCH-M-ARMA models to measure
spillover and leverage effects in the futures ETFs. ETF returns have a strong impact on their
underlying index returns, which helping investors and fund managers to consider an important
indicator to perform their investment strategy. The past literature like Diaz and Nguyen (2014),
Chen and Diaz (2015) and Nguyen and Diaz (2016) consistently used the ARFIMA-
FIAPARCH model to detect in different ETFs and found asymmetric fluctuations.
Regarding long-term memory in an ETF, Chen and Diaz (2013), Chen and Huang (2014),
and Chen and Maya (2016) used ARFIMA-FIGARCH model to explore whether there is long-
term memory of fluctuations. In different ETF commodities, it is found that fluctuations have
a long-term memory structure.
There are also financial products, Exchange-Traded Note (ETN) which is similar to an
ETF, discussed by scholars. Chen and Diaz (2017) used ARFIMA-FIGARCH models and
tested the long-term memory and the chaotic effect for currency ETN. The results revealed that
the volatility of the currency ETN has a long memory and irreversible effect. Chen and Diaz
(2016) used the Granger causality test and MGARCH models to study the exchange rate of
Futures ETN. They explored volatility dynamics and the correlation for corresponding futures
contract returns. Most lagging ETNs are the main indicator of the present value of futures
contracts. The results showed that there was long-term sustainability, and the fluctuation of
ETN yield has an impact on its futures contracts.
There are also applications in different sectors. Based on the analysis of precious metals
(base metals) ETF, Chen and Trang (2017) used MGARCH models to test the volatility. The
results showed that the return fluctuations of the precious metal (base metal) ETF affected its
futures earnings. Chen, Batsukh, and Huang (2018) applied for eight agricultural ETFs and
examined whether ETFs were consistent with the chaotic effects of potential random data. The
results of GARCH provided an overview of financial insights in the field of agricultural ETF
investment forecasting to eliminate trading sentiment while providing investors with
considerable profitability experience. Furthermore, Chiu, Chung, Ho, and Wang (2012) used
14 financial ETFs to explore the relationship between them. During the subprime crisis, it was
found that the increase in actual liquidity could be improved. Good liquidity has a greater
impact on financial ETFs than the index. Dannhauser (2017) found that the use of liquidity
testing on corporate bond ETFs has significant and long-term positive valuation impacts on
financial innovation.
3. Data and Methodology
This study selected from Fintech, Financial, and Technology ETFs. The data period was
obtained from Yahoo Finance from September 16, 2016, to January 17, 2019, with 588
24 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
observations for each ETF. From Table 1, three types of ETFs and inception date were
presented.
Table 1 FinTech ETF, Financial ETF and Technology ETF data
Types Exchange Traded Funds Ticker Inception Date
FinTech
ARK Web x.0 ETF ARKW Sep. 30, 2014
Global X Robotics & Artfcl Intelligence ETF BOTZ Sep. 12, 2016
EMQQ Emerging Markets Intrnt & Ecmrc ETF EMQQ Nov. 12, 2014
Global X FinTech ETF FINX Sep. 12, 2016
ETFMG Prime Mobile Payments ETF IPAY Jul. 15, 2015
First Trust Cloud Computing ETF SKYY Jul. 06, 2011
Global X Internet of Things ETF SNSR Sep. 12,2016
Financial
Fidelity MSCI Financials ETF FNCL Oct. 21, 2013
Direxion Daily Financial Bull 3X ETF FAS Nov. 06, 2008
First Trust Financials AlphaDEX ETF FXO May. 08, 2007
SPDR S&P Bank ETF KBE Nov. 08, 2005
SPDR S&P Insurance ETF KIE Nov. 08, 2005
Financial Select Sector SPDR ETF XLF Dec. 16, 1998
SPDR Wells Fargo Preferred Stock ETF PSK Sep. 16, 2009
Technology
Technology Select Sector SPDR ETF XLK Dec. 16, 1998
Vanguard Information Technology ETF VGT Jan. 26, 2004
VanEck Vectors Semiconductor ETF SMH Dec. 20, 2011
iShares US Technology ETF IYW May. 15, 2000
iShares Expanded Tech-Software Sect ETF IGV Jul. 10, 2001
iShares Global Tech ETF IXN Nov. 12, 2001
iShares Expanded Tech Sector ETF IGM Mar. 13, 2001
Organized from the MoneyDJ financial website. (www.moneydj.com)
3.1 Auto-Regressive and Moving Average Model (ARMA) model
Box and Jenkins (1976) created a self-regressive moving average model, and the ARMA
model expressed the relationship between the current variable of the time series and the past
variables. The AR model shows that the variable y𝑡 is not only affected by the error term 𝜀𝑡, but
also affected by the early stage of its own variables.
The generalized model configuration of AR(p) is:
y𝑡 = 𝑎0 + ∑ 𝑎𝑖𝑦𝑡−𝑖 + 𝜀𝑡𝑝𝑖=1 , (1)
where 𝑎0 is a constant intercept term; p represents the number of backward periods (lag); 𝑎𝑖
stand for the coefficient of 𝑦𝑡−𝑖; 𝜀𝑡 stands for white noise.
The MA model is a characteristic of implicit error correction. The variable y𝑡 has some
correlation with the error term (𝜀𝑡−1, 𝜀𝑡−2,…) in the early stage of the variable.
The generalized model of MA(q) is configured as:
25 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
y𝑡 = 𝑎0 + 𝜀𝑡 + ∑ 𝑏𝑖𝜀𝑡−𝑖𝑞𝑖=1 , (2)
where 𝑎0 denotes a constant intercept term; p is the number of backward periods (lag); 𝑎𝑖
represents the coefficient of 𝑦𝑡−𝑖; 𝜀𝑡 is white noise.
As for the ARMA(p,q) model, the representation is:
y𝑡 = 𝑎0 + ∑ 𝑎𝑖𝑦𝑡−𝑖𝑝𝑖=1 + 𝜀𝑡 + ∑ 𝑏𝑖𝜀𝑡−𝑖
𝑞𝑖=1 . (3)
Note that the model is divided into symmetry and asymmetry effects. The two symmetry
is ARCH and GARCH models. The asymmetric effect contains three models, that is EGARCH,
GJR and jumps models. Thus, their models are used to measure the asymmetry and volatility
among FinTech, Financial, and Technology ETFs.
3.2 Symmetric Model
3.2.1 Autoregressive Conditional Heteroskedasticity (ARCH) model
In the past classic models, the residual variability was fixed, and Engle (1982) proposed
that the ARCH model changes over time and can explain many econometric problems. The
conditional variability of the ARCH model is affected by the square of the residual term of the
past q period (unexpected volatility). It means that the conditional variability can be changed at
any time. The ARCH(q) model is expressed as follows:
y𝑡|ψ𝑡−1~𝑁(𝑥𝑡𝛽, ℎ𝑡) (4)
ℎ𝑡 = ℎ(ε𝑡−1, ε𝑡−2, … , ε𝑡−𝑞 , 𝛼), (5)
𝜀𝑡 = 𝑦𝑡 − 𝑥𝑡𝛽,
According to the ARCH model, y𝑡 is the time series data. ψ𝑡−1
provides all information in
period 1 to t-1. ℎ𝑡 is the y𝑡 conditional variation affected by the residual term of the previous q.
𝛼, 𝛽 is an unknown parameter. q represents the order of the ARCH process. 𝑥𝑡𝛽 denotes a linear
set containing the generation variables and exogenous variables in the backward period of the
message set.
The conditional residual is parameterized to obtain a non-negative value. Rearrange (5):
ℎ𝑡 = 𝛼0 + 𝛼1𝜀𝑡−12 + 𝛼2𝜀𝑡−2
2 + ⋯ + 𝛼𝑞𝜀𝑡−𝑞2 = 𝑍𝑡
′𝛼 , (6)
𝑍𝑡′ = (1, 𝜀𝑡−1
2 , 𝜀𝑡−22 , … , 𝜀𝑡−𝑞
2 ),
α = (𝛼0, 𝛼1, … , 𝛼𝑞),
𝛼0 > 0, 𝛼𝑖 > 0, 𝑖 = 1,2, … , 𝑞.
where ℎ𝑡 is the current condition change due to the surplus in the previous period, meaning that
there is fluctuation clustering. Thus, the current period residuals are very large, and the current
period will fluctuate in the same direction, and vice versa.
3.2.2 Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model
26 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
ARCH model created by Engle (1982) was one of the most important contributors to
Financial Econometrics. Engle and Bollerslev (1986) added the delayed backward to the ARCH
model to derive GARCH, as follows:
𝑦𝑡 = 𝑏𝑥𝑡 + 𝜀𝑡,
𝜀𝑡 = 𝑦𝑡 − 𝑏𝑥𝑡, (7)
𝜀𝑡|ψ𝑡−1~𝑁(0, ℎ𝑡),
ℎ𝑡 = 𝜔 + ∑ 𝛼𝑗𝜀𝑡−12 + ∑ 𝛽𝑖ℎ𝑗−1
2𝑝𝑖=1 = 𝑎0 + 𝐴(𝐿)𝜀𝑡
2𝑞𝑗=1 + 𝐵(𝐿)ℎ𝑡
2,
q ≥ 0, p ≥ 0,
𝛼0 > 0, 𝛼𝑗 > 0, 𝑗 = 1,2, … , 𝑞,
𝛽𝑖 > 0, 𝑖 = 1,2, … , 𝑝,
where 𝑦𝑡 is the time series data by the GARCH model. ψ𝑡−1
s provides all information in the
period t to t-1 period. ℎ𝑡 represents the y affected by the square of the residual q of the previous
period and the conditional variation of the previous period. The conditional variation number
is the unknown parameter vector, which is the conditional average of 𝑦𝑡. q is the order of the
ARCH process, and p denotes the order of the GARCH process. It can be known that when p=0,
GARCH (p,q) will be returned. In the form of ARCH(q), if p=q=0, the residual term is a white
noise process.
3.3 Asymmetric Model
3.3.1 Exponential Generalized Autoregressive Conditional Heteroskedasticity
(EGARCH) Model
Nelson (1991) proposed the EGARCH model as follows:
ln( σ𝑡2) = 𝜔 + 𝛽ln(σ𝑡−1
2 ) +α |𝜇𝑡−1
𝜎𝑡−1− √
2
𝜋| + 𝛾
𝜇𝑡−1
𝜎𝑡−1 . (8)
It is assumed that γ < 0 indicates that there is a leverage effect. If 𝛾 ≠ 0, there is an
asymmetry effect.
3.3.2 Glosten, Jagannathan and Runkle (GJR) model
This model is offered by Glosten, Jagannathan, and Runkle (1993) and its generalized
version is as follows:
σ𝑡2 = 𝜔 + ∑ 𝛼𝑖
𝑞𝑖=1 𝜀𝑡−𝑖
2 + ∑ 𝛾𝑖𝑞𝑖=1 𝑆𝑡−𝑖
− 𝜀𝑡−𝑖2 + ∑ 𝛽𝑗𝜎𝑡−𝑗
2𝑝𝑗=1 , (9)
where 𝑆𝑡−𝑖− is a dummy variable that takes the value 1 when 𝛾𝑖 is negative, and the value 0
otherwise.
27 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
3.3.3 Jumps Model
In most financial time series, when the standard GARCH model encountered excessive
kurtosis, it cannot be fully explained. The jump-diffusion and stochastic volatility models are
used to overcome this deficiency. The following jump-diffusion process is as follows:
dp(t) = μ(t)dt + σ(t)dW(t) + κ(t)dp(t), 0 ≤ t ≤ T, (10)
where μ(t) is a continuous partial variation process. σ(t) represents a strictly random wave
process. W(t) stands for a standard Brownian motion. dp(t) is a counting process equal to one
when a jump occurs at time t, and 0 otherwise. The jump intensity denotes 𝑙(t) and κ(t) is the
size of the jump.
This study assumed jumps in stock prices following a probability law. By following a
Poisson distribution, the jumps are a continuous-time discrete process. For a given time t, let
X𝑡 be the number of times, a special event occurs during the time period [0, t]. Then X𝑡 follows
a Poisson distribution if:
Pr(X𝑡 = m) =𝑙𝑚𝑡𝑚
𝑚!exp(−𝑙t) , 𝑙 > 0. (11)
The 𝑙 parameter stands for the occurrence of the special event. It refers to as the rate or
intensity of the process. Noted that E(X𝑡) = 𝑙. Simulating a continuous-time GARCH diffusion
processes with jumps, as follows:
dp(t) = σ(t)dW𝑝(𝑡) + κ(𝑡)𝑑𝑞(𝑡), (12)
dσ2(t) = θ[ω − σ2(𝑡)]𝑑𝑡 + (2𝜆𝜃)1
2𝜎2(𝑡)𝑑𝑊𝑑(𝑡), (13)
κ(𝑡)~ N(0, σ𝑘2),
dp(𝑡)~Poisson(𝑙).
By providing a reliable nonparametric value of the price change, Andersen and Bollerslev
(1998) achieved discrete volatility. The use of realized volatility is to convey continuous time.
The use of realized volatility is to convey continuous time. The daily realized volatility is
calculated as the sum of the returns with the day of the trading day. The simulated daily
volatility of ∆-period return and r𝑡,∆ ≡ 𝑟(𝑡, ∆) ≡ 𝑝(𝑡) − 𝑝(𝑡 − ∆). The daily time interval can
be normalized to unity, that is r𝑡+1,1 = r𝑡+1. The daily realized volatility of day 𝑡, denoted
RV𝑡+1(∆) and not 𝑅𝑉𝑡(∆) because it allows to compute at the end of day t, which is then
presented as follows:
RV𝑡+1(∆) ≡ ∑ 𝑟𝑡+𝑗∆,∆21/∆
𝑗=1 . (14)
When ∆→ 0
RV𝑡+1(∆) → ∫ 𝜎2(𝑖)𝑑𝑖𝑡+1
𝑡. (15)
The achieved volatility is a combination of fluctuations without jumping, but not in the
case of a jump. Therefore, it is useful to discrete the two components of the second variation
process. By using a bi-power variation measurement, which is a consistent estimate of the
28 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
integral volatility at the time of the jump can be measured by Barndorff-Nielsen and Shephard
(2004) and Barndorff-Nielsen and Shepard (2005). The bi-power variation (BV) is defined as:
𝐵𝑉𝑡+1(Δ) ≡ μ1−2 ∑ |𝑟𝑡+𝑗Δ, Δ||𝑟𝑡+(𝑗−1)Δ, Δ|
1/Δ𝑗=2 , (16)
where Δ is small in increments time.
Rather than deleting the sum of the squared returns, the product of adjacent absolute
returns and the probability of discontinuity will be disappearing in the limit. Quadratic variable
estimation discontinuities by Barndorff-Nielsen and Shephard (2004):
RV𝑡+1(Δ) − BV𝑡+1(Δ) ⟶ ∑ 𝑘2(𝑖)𝑡<𝑖≤𝑡+1 , (17)
where RV is realized variability. And imposing non-negativity can be measured as:
J𝑡+1(Δ) ≡ max [𝑅𝑉𝑡+1(Δ) − 𝐵𝑉𝑡+1(Δ), 0]. (18)
4. Empirical Findings
Descriptive statistics are the characteristics of the group using statistical statistic. The
common ones are the mean, standard deviation, minimum, and maximum. The average is a
statistic that describes the degree of data concentration by dividing the sum of a set of samples
by the number of samples. The standard deviation (Std. Dev.) is used to measure the degree of
dispersion of a set of values. The smaller the value, the smaller the difference between the
individual samples. The larger the value, the larger the difference between the individual
samples. In descriptive statistics (Table 2), each group has the average standard deviation, such
as Panel A (FinTech ETF) 1.2239, Panel B (Financial ETF) 1.1322 and Panel C (Technology
ETF) 1.2091 to It can be known that FinTech ETF has the largest indicating a high degree of
volatility.
In addition, whether the data is normal distribution can be observed by the Skewness
coefficient, Kurtosis coefficient, and Jarque-Bera statistic. The Skewness coefficient shows that
the ETFs are all left-biased. In terms of Kurtosis coefficient, all ETFs are leptokurtic
distribution. Finally, the Jarque-Bera statistic is 1% significant so that it can be found as a
normal distribution.
Table 3 revealed the various test results for each ETF. The Augmented Dickey-Fuller
(ADF) test was tested to determine stationary, and all samples showed significance
(stationarity). The minimum Akaike Information Criterion (AIC) value based on the maximum
(3, 3) order levels was used to identify ARMA, GARCH, EGARCH, and GJR-GARCH models.
The Breush-Godfry LM test tested the sequence correlation, and the results showed that the
return hypothesis for all ETFs could not be rejected. The ARCH effect is tested using the
Lagrange Multiplier test (ARCH-LM), where the ARCH error in the residual is eliminated for
all ETF for GARCH models. The null hypothesis of the ARCH effect is not accepted. Chen and
Diaz (2012) examined the faith-based and non-faith-based ETF returns to find the order level
for ARMA models in order to decide the minimum value of Akaike Information Criterion (AIC).
By adopting pre-ARCH-LM and post-ARCH-LM tests to remove error terms in ARMA-
GARCH, they found that the results rejected the null hypothesis.
29 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
The ARMA-GARCH orders listed in Table 4. It indicates the influence of GARCH
fluctuations with the different order levels. It is found that most of α+β is close to 1, indicating
that the fluctuation rate of each frequency is highly persistent. Radha and Thenmozhi (2006)
established an appropriate model to predict short-term interest rates and found that the GARCH
model is more suitable for prediction than other models because of the clustering volatility.
This study utilizes EGARCH, GJR-GARCH, and jump models to conduct empirical work for
determining asymmetry in the ETFs.
30 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 2 Descriptive Statistics of FinTech ETF
Panel A: FinTech ETF
ETF code ARKW BOTZ EMQQ FINX IPAY SKYY SNSR
Mean 0.1388 0.0345 0.0160 0.0788 0.0722 0.0758 0.0233
Std. Dev. 1.4957 1.1462 1.4989 1.1745 1.0430 1.0471 1.1618
Median 0.2189 0.0825 0.0934 0.1602 0.1693 0.0908 0.0786
Maximum 6.1481 4.3856 6.0582 5.2210 4.9304 5.3220 6.6056
Minimum -5.9122 -6.1179 -5.1143 -6.3460 -5.0377 -4.4578 -5.9968
Skewness -0.3129 -0.7771 -0.1662 -0.8463 -0.6373 -0.3607 -0.3315
Kurtosis 5.3998 7.0223 4.3140 7.7093 7.3452 6.3657 7.2232
Jarque-Bera 150.4387*** 454.7853*** 44.9353*** 612.5018*** 501.5311*** 289.7963*** 446.9778***
Panel B: Financial ETF
ETF code FAS FNCL KBE FXO KIE PSK XLF
Mean 0.1106 0.0455 0.0467 0.0330 0.0353 -0.0163 0.0489
Std. Dev. 2.5648 1.0166 1.2319 0.8287 0.8482 0.3715 1.0635
Median 0.1694 0.0696 0.1038 0.0684 0.0671 0.0221 0.0409
Maximum 12.7354 4.2264 5.0234 4.4878 3.8170 2.5555 4.4276
Minimum -14.0237 -4.9247 -5.4719 -3.9286 -3.7862 -2.3417 -5.1724
Skewness -0.7373 -0.3841 -0.2770 -0.5160 -0.4955 -0.5716 -0.3935
Kurtosis 7.7222 6.1714 5.3273 7.3370 6.5170 12.2526 6.2256
Jarque-Bera 598.5794*** 260.4279*** 139.9755*** 486.1009*** 326.5551*** 2125.8720*** 269.6271***
Panel C: Technology ETF
ETF code IGM IGV IXN IYW SMH VGT XLK
Mean 0.0697 0.0872 0.0548 0.0597 0.0526 0.0650 0.0528
Std. Dev. 1.1754 1.2531 1.1340 1.1783 1.4507 1.1410 1.1310
Median 0.1302 0.1105 0.1497 0.1288 0.2162 0.1325 0.1187
Maximum 6.1809 6.3108 5.4165 6.3245 5.4678 5.8643 5.8642
Minimum -5.0821 -5.5548 -5.1166 -4.9350 -6.9473 -5.0685 -5.1786
Skewness 1.1754 1.2531 1.1340 1.1783 1.4507 1.1410 1.1310
Kurtosis -0.5185 -0.4523 -0.5737 -0.4831 -0.7236 -0.5800 -0.5714
Jarque-Bera 461.2822*** 304.1741*** 368.4276*** 426.6591*** 240.5238*** 450.7930*** 546.6392***
Note: *, **, and *** are significant at 10, 5, and 1%, respectively.
31 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 3 FinTech ETF, Financial ETF and Technology ETF - Summary Statistics of Unit Root,
LM, and ARMA-LM Testing for ETF and Index Returns
Panel A: FinTech ETF
ETF code ARKW BOTZ EMQQ FINX IPAY SKYY SNSR
ADF -23.5732*** -22.0626*** -22.2564*** -23.1093*** -24.3545*** -24.6483*** -26.8035***
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
ARMA (0,0) (2,3) (2,2) (3,2) (2,3) (2,2) (2,1)
AIC 3.6480 3.1008 3.6353 3.1607 3.1607 2.9253 3.0209
LM 0.8717 3.4613 1.9394 1.7560 1.7560 1.4393 3.8561
(0.9286) (0.4838) (0.7469) (0.7805) (0.7805) (0.8373) (0.4258)
Per-
ARCH-LM
26.1363*** 16.4140*** 1.9394 7.4094*** 7.4094*** 10.5134*** 22.9229***
(0.0000) (0.0001) (0.7469) (0.0065) (0.0065) (0.0012) (0.0000)
GARCH (2,1) (1,1) (2,2) (0,1) (0,1) (1,1) (1,1)
AIC 3.4273 2.7864 3.5251 2.8671 2.8671 2.6788 2.8863
Post-
ARCH-LM
0.0148 0.0148 0.0011 2.0307 2.0307 0.4785 0.2751
(0.9032) (0.9032) (0.9733) (0.1542) (0.1542) (0.4891) (0.5999)
Panel B: Financial ETF
ETF code FAS FNCL KBE FXO KIE PSK XLF
ADF -23.9931*** -23.4311*** -23.4237*** -23.7115*** -23.5974*** -20.5330*** -23.8722***
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
ARMA (2,2) (2,2) (3,2) (2,2) (3,3) (1,0) (2,2)
AIC 4.7107 2.8700 3.2359 2.4610 2.5004 0.8370 2.9625
LM 0.7180 2.2351 6.7682 2.5975 2.1714 7.6021 3.0868
(0.6984) (0.6926) (0.1487) (0.6273) (0.7043) (0.1073) (0.5434)
Per-
ARCH-LM
29.3100*** 17.7141*** 7.30081*** 14.5410*** 30.2805*** 11.2655*** 20.2554***
(0.0000) (0.0000) (0.0069) (0.0001) (0.0000) (0.0008) (0.0000)
GARCH (2,2) (1,1) (2,1) (1,1) (2,2) (1,1) (1,2)
AIC 4.5228 2.7800 3.2193 2.2773 2.3637 0.6685 2.8508
Post-
ARCH-LM
0.8655 0.0294 0.0057 0.9038 0.3602 0.0780 0.3055
(-0.0293) (0.8639) 0.903804 (0.3418) (0.5484) (0.7801) (0.5804)
Panel C: Technology ETF
ETF code IGM IGV IXN IYW SMH VGT XLK
ADF -25.7774*** -25.0650*** -25.9264*** -25.9444*** -26.6696*** -25.7498*** -26.2023***
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
ARMA (2,2) (3,3) (2,2) (2,2) (2,2) (2,2) (2,3)
AIC 3.1382 3.2849 3.0612 3.1457 3.5729 3.0801 3.0650
LM 2.1856 0.9326 1.3027 4.2112 0.9663 3.4837 2.6809
(0.7017) (0.9198) (0.8609) (0.3782) (0.9149) (0.4804) (0.6126)
Per-
ARCH-LM
19.1705*** 11.8979*** 31.0319*** 23.4392*** 7.0568*** 26.8709*** 35.4840***
(0.0000) (0.0006) (0.0000) (0.0000) (0.0079) (0.0000) (0.0000)
GARCH (2,2) (2,1) (1,1) (2,2) (1,1) (1,1) (1,1)
AIC 2.8321 3.0572 2.7645 2.8560 3.4258 2.7751 2.7013
Post-
ARCH-LM
0.2148 0.0414 0.0985 0.4794 0.1285 0.0332 0.0361
(0.6430) (0.8389) (0.7536) (0.4887) (0.7200) (0.8554) (0.8493)
Note:1. *, **, and *** are significant at 10, 5, and 1%, respectively.
2. 0.0000 here means the number is less than 0.0001.
32 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 4 ARMA-GARCH of FinTech ETF, Financial ETF and Technology ETF
Part A: FinTech ETF
ETF code ARKW BOTZ EMQQ FINX IPAY SKYY SNSR
ARMA/ (0,0)/ (2,3)/ (2,2)/ (3,2)/ (2,3)/ (2,2)/ (2,1)/
GARCH (2,1) (1,1) (2,2) (0,1) (1,1) (1,1) (1,1)
0.9755 0.9485 0.9773 1.0119 1.0108 0.9595 0.9182
Part B: Financial ETF
ETF code FAS FNCL KBE FXO KIE PSK XLF
ARMA/ (2,2)/ (2,2)/ (3,2)/ (2,2)/ (3,3)/ (1,0)/ (2,2)/
GARCH (2,2) (1,1) (2,1) (1,1) (2,2) (1,1) (1,2)
0.9913 0.7803 0.5094 0.9476 0.9841 0.7388 0.3491
Part C: Technology ETF
ETF code IGM IGV IXN IYW SMH VGT XLK
ARIMA/ (2,2)/ (3,3)/ (2,2)/ (2,2)/ (2,2)/ (2,2)/ (2,3)/
GARCH (2,2) (2,1) (1,1) (2,2) (1,1) (1,1) (1,1)
0.9109 0.9707 0.9707 0.994 0.9786 0.9786 0.9586
4.1 EGARCH Model Analysis
In Table 5, 21 ETFs in the FinTech ETF, Financial ETF, and Technology ETF are used
for optimal model hierarchy and parameter estimation. The EGARCH model estimates from
γ<0, γ≠0, and statistically significant P values of 1%. Except for the EMQQ ETF, all the null
hypotheses of the FinTech ETF, Financial ETF, and Technology ETF were rejected. There is a
wave of asymmetry in the form of expression. Chen and Kuan (2002) pointed out that the
irreversible effects of the US stock indexes were examined. It was found that the asymmetry of
the EGARCH model was captured in the regular sequence, confirming that the time
irreversibility can be attributed to the volatility asymmetry.
The empirical results have a negative impact due to the coefficient of γ, revealling that
there is a leverage effect. When the investment amount increases, the investor bears a greater
risk. If the γ is positive, it will produce an inverse leverage effect. Bowden and Payne (2008)
found that the positive impact on electricity prices seems to have the greatest impact on the
volatility. Suleman (2012) analyzed the volatility of political news on stock market returns. The
results found that KSE100 index returns would be stronger (almost twice) because the impact
of bad news about the news was greater than the good news.
4.2 GJR GARCH Model Analysis
When testing with the GJR model, the verification results should be significant, and further
exploration is whether there is leverage effect, and the limit ω ≥ 0, α1 ≥ 0, β1 ≥ 0 𝑎𝑛𝑑 α1 +
𝛾1 ≥ 0. In the conditional expression, when there is good news : 𝜀𝑡−1 > 0 and bad news:
𝜀𝑡−1 < 0, while β1 affects the good news associated with α1 + 𝛾1. When 𝛾1 > 0, it indicates
that there will be a negative impact leading to greater shock fluctuations.
33 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 5 EGARCH-ARMA of FinTech ETF, Financial ETF and Technology ETF
Part A: FinTech ETF
ETF code ARKW BOTZ EMQQ FINX IPAY SKYY SNSR
ARMA/
EGARCH (0,0)/ (2,1) (2,3)/ (1,1) (2,2)/ (2,2) (3,2)/ (0,1) (2,3)/ (1,1) (2,2)/ (1,1) (2,1)/ (1,1)
γ
-0.0773*** -0.1077*** -0.0518* -0.2054*** -0.1660*** -0.1847*** -0.0992***
(0.0008) (0.0000) (0.1000) (0.0000) (0.0000) (0.0000) (0.0000)
Part B: Financial ETF
ETF code FAS FNCL KBE FXO KIE PSK XLF
ARMA/
EGARCH (2,2)/ (2,2) (2,2)/ (1,1) (3,2)/ (2,1) (2,2)/ (1,1) (3,3)/ (2,2) (1,0)/ (1,1) (2,2)/ (1,2)
γ
-0.2257*** -0.1247*** -0.0982*** -0.1445*** -0.1295*** -0.1213*** -0.0891***
(0.0000) (0.0000) (0.0008) (0.0000) (0.0009) (0.0000) (0.0011)
Part C: Technology ETF
ETF code IGM IGV IXN IYW SMH VGT XLK
ARMA/
EGARCH (2,2)/ (2,2) (3,3)/ (2,1) (2,2)/ (1,1) (2,2)/ (2,2) (2,2)/ (1,1) (2,2)/ (1,1) (2,3)/ (1,1)
γ -0.2130*** -0.1753*** -0.1608*** -0.1711*** -0.0616*** -0.1506*** -0.1623***
(0.0000) (0.0000) (0.0000) (0.0034) (0.0035) (0.0000) (0.0000)
Note:1. *, **, and *** are significant at 10, 5, and 1%, respectively.
2. 0.0000 here means the number is less than 0.0001.
In Table 6, there are positively significant results for the FinTech ETF of Panel A – IPAY,
SKYY, SNAR, and FINX. In Panel B, the results showed that there are positively significantly
in Financial ETF – KIE, FXO, FNCL, and XLF. Finally, there is positively significance for
Panel C for Technology ETF – IXN, IYW, VGT, XLK. As a result, the asymmetric effect does
exist. Further, added to a limit condition that Panel A-FINX; Panel B - FNCL, FXO, KIE and
XLF; and Panel C-XLK have leverage effect. The empirical results showed that panel B
(Financial) ETFs has the best asymmetric volatility comparing to FinTech and Technology
ETFs. It indicates that the negative effects (bad messages) were the cause of the asymmetry.
Sakthivel, VeeraKumar, Raghuram, Govindarajan, and Anand (2014) studied the impact of the
financial crisis on the volatility of the Indian stock market. They analyzed the financial crisis
before and after the financial crisis. By using the GJR-GARCH model, the results indicated that
the asymmetry fluctuations were very large.
34 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 6 GJR GARCH of FinTech ETF, Financial ETF and Technology ETF
Panel A: FinTech ETF
ETF code ARKW BOTZ EMQQ FINX IPAY SKYY SNSR
ARMA/GARCH (0,0)/ (2,1) (2,3)/ (1,1) (2,2)/ (2,2) (3,2)/ (0,1) (2,3)/ (1,1) (2,2)/ (1,1) (2,1)/ (1,1)
ω 0.0908 0.0691 0.0812 0.5576 0.0418*** 0.0619*** 0.0459*
(0.1732) (0.1546) (0.3583) (0.1372) (0.0034) (0.0042) (0.0693)
α1 0.0644 0.0973 0.0391 0.0362 -0.1018*** -0.0211 -0.0140
(0.4002) (0.2757) (0.3342) (0.4812) (0.0000) (0.4353) (0.6165)
β1 0.8338*** 0.7504*** 0.0155 0.7626*** 0.9081*** 0.8226*** 0.9019***
(0.0000) (0.0000) (0.7818) (0.0000) (0.0000) (0.0000) (0.0000)
γ1 0.1322 0.1868 -0.0269 0.2247* 0.2629*** 0.2525*** 0.1282**
(0.1917) (0.1051) (0.6437) (0.0501) (0.0000) (0.0023) (0.0401)
α + β + (γ
2) 0.9553 0.9411 0.9603 0.9112 0.9378 0.9278 0.9520
Panel B: Financial ETF
ETF code FAS FNCL KBE FXO KIE PSK XLF
ARMA/GARCH (2,2)/ (2,2) (2,2)/ (1,1) (3,2)/ (2,1) (2,2)/ (1,1) (3,3)/ (2,1) (1,0)/ (1,1) (2,2)/ (1,2)
ω 0.6655 0.2258** 0.4604* 0.0248 0.0519* 0.0163 0.2051*** (0.4013) (0.0108) (0.0559) (0.1889) (0.0542) (0.4088) (0.0084)
α1 0.0100 0.0735 0.0677 0.0239 0.0066 0.0061 0.0721* (0.7593) (0.1375) (0.3543) (0.4304) (0.8676) (0.8918) (0.0909)
β1 0.2083 0.6071*** 0.5065 0.8611*** 0.1983 0.7613*** 0.8989*** (0.3928) (0.0000) (0.5455) (0.0000) (0.4809) (0.0017) (0.0009)
γ1 0.3582 0.1994* 0.1357 0.1501** 0.2243*** 0.1859 0.1705* (0.194) (0.0708) (0.4721) (0.0355) (0.0091) (0.2164) (0.0628)
α + β + (γ
2) 0.8892 0.7802 0.6942 0.9601 0.9192 0.8604 0.8224
Panel C: Technology ETF
ETF code IGM IGV IXN IYW SMH VGT XLK
ARMA/GARCH (2,2)/ (0,1) (3,3)/ (1,1) (2,2)/ (1,1) (2,2)/ (2,2) (2,2)/ (1,1) (2,2)/ (1,1) (2,3)/ (0,1)
ω 0.8465*** 0.1041** 0.0481*** 0.0196 0.0732 0.0656*** 0.5790***
(0.0000) (0.0482) (0.0069) (0.2244) (0.1682) (0.0009) (0.0000)
α1 0.2313 -0.0140 -0.0409 -0.0577*** 0.0252 -0.0511 0.2643
(0.3883) (0.7206) (0.1758) (0.0000) (0.549) (0.1552) (0.1515)
β1
0.8187*** 0.8678*** 1.4923*** 0.8958*** 0.8505***
(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
γ1 0.4634 0.2272** 0.2248*** 0.2885*** 0.0745 0.2607*** 1.2074**
(0.1241) (0.0203) (0.0011) (0.0002) (0.3753) (0.0001) (0.0121)
α + β + (γ
2) 0.4630 0.9183 0.9393 0.9807 0.9583 0.9297 0.8679
Note:1. *, **, and *** are significant at 10, 5, and 1%, respectively. 2. 0.0000 here means the number is less than 0.0001.
35 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
4.3 Jump GARCH Model Analysis
This paper examined the difference between the realized volatility (RV) and bi-power
variation (BV), which is called realized jump (RJ). If the data exists realized jump, it is an
asymmetric effect on ETF data. Descriptive statistics and Ljung-Box Q statistics based on Jump
were listed in Table 7. The median of each ETF is less than the average. The standard deviation
is between 4 and 13. The results showed that Financial ETFs have a large value in standard
deviation, and the maximum of RJ is approximate 150 and a minimum of 0. Therefore, the jump
is large compared to others. Wang and Huang (2012) explored the Hu-Shen 300 index. They
found that the Ljung-Box statistics ln(RV) and ln(BV) have strong persistence (large value)
characteristics, while jump has a small persistence (small value). The Ljung-Box Q statistic
value is between 4 and 12. The value is small, and the P-value is not self-related, indicating that
the jump effect has little persistence.
With observation value in 60-day return rate, the jump effect of Group A: FinTech ETF
shows that the jump rate of BOTZ and SKYY is 31.67%, which is the best effect of discrete
jumps. In Panel B: Financial ETF has a jumping effect, in which the PSK hopping frequency
of the discrete hopping group is 40%. Panel C: Technology ETF has a hopping effect, in which
the IGM hopping rate of 41.67% is the most aggregated and the highest value. Among the three
groups, the results found that discrete hops with the highest frequency is Technology ETF.
4.4 Group Integration Comparison
In Table 8, the empirical results revealed the comparison of Panel A: FinTech ETF, Panel
B: Financial ETF and Panel C: Technology ETF. After using ARMA combined with GARCH
to find the most appropriate level, this study examined price fluctuations and further tested for
asymmetric effects. Chen and Kien (2019) were investigating whether high-yield and low-yield
dividend ETFs have this spillover and leverage effects to find the best residual for ARMA-
GARCH based on the ARCH-LM test. This study completely removed the residuals to find the
most suitable combination in all Panels. This paper also applies EGARCH model to analyze the
variation of the conditional mean and asymmetry responding in the conditional variance. The
empirical results found that the leverage effect does exist due to all negative γ are significant at
1%, 5%, and 10% signification level. It indicated that good news experienced less volatility
than bad news in the suffering time.
GJR-GARCH and EGARCH can be used to investigate whether there is a leverage effect.
The only difference is that the GJR-GARCH model can further distinguish the difference
between good and bad news on data fluctuation. The result showed that Financial ETF was
mostly connected with the asymmetric effect, meaning that the bad news will be greater than
the good news at different times. Finally, the results of the jump model found that Technology
ETF has the highest probability of jumping, indicating the most jumping aggregation effect
based on the Ljung-Box Q test. The statistic indicates that this aggregation effect last for short
periods. The statistic indicates that this aggregation effect last for short periods.
36 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 7 Realized Jump (RJ) GARCH of Descriptive Statistics
Panel A: FinTech ETF
NO. ARKW BOTZ EMQQ FINX IPAY SKYY SNSR
Mean 2.649 3.335 3.138 3.168 2.28 2.742 3.319
Maximum 25.129 32.505 47.481 34.233 16.854 22.447 41.446
Minimum 0 0 0 0 0 0 0
Std. Dev. 6.578 6.589 8.135 6.6 4.346 4.875 8.119
Skewness 2.334 2.363 3.535 2.836 1.945 1.938 3.072
Kurtosis 6.936 8.709 17.127 11.837 5.841 6.592 12.601
Observations 60 60 60 60 60 60 60
Q (10) 7.849 9.592 7.501 7.532 12.106 9.45 4.001
(0.644) (0.477) (0.677) (0.674) (0.278) (0.49) (0.947)
Jump Ratio 16.67% 31.67% 21.67% 30.00% 30.00% 31.67% 11.67%
Panel B: Financial ETF
NO. FAS FNCL KBE FXO KIE PSK XLF
Mean 16.667 2.177 1.995 1.928 1.541 2.28 4.054
Maximum 150.36 17.595 29.122 19.687 14.699 16.854 35.959
Minimum 0 0 0 0 0 0 0
Std. Dev. 32.476 4.251 5.82 4.004 3.261 4.346 6.905
Skewness 2.344 2.021 3.113 2.6 2.455 1.945 2.185
Kurtosis 8.3 6.299 12.232 10.013 8.62 5.841 9.022
Observations 60 60 60 60 60 60 60
Q (10) 3.267 5.912 9.81 4.737 7.975 12.106 4.237
(0.974) (0.823) (0.457) (0.908) (0.631) (0.278) (0.936)
Jump Ratio 33.33% 28.33% 13.33% 30.00% 26.67% 40.00% 30.00%
Panel C: Technology ETF
NO. IGM IGV IXN IYW SMH VGT XLK
Mean 4.064 3.252 3.207 3.899 3.386 3.956 2.285
Maximum 38.106 31.514 32.328 42.082 37.182 36.527 18.9
Minimum 0 0 0 0 0 0 0
Std. Dev. 7.006 7.084 5.936 7.341 7.764 7.037 4.578
Skewness 2.445 2.479 2.475 2.825 2.546 2.277 2.188
Kurtosis 10.686 8.539 10.925 13.494 9.241 9.235 7.111
Observations 60 60 60 60 60 60 60
Q (10) 3.451 3.451 9.81 2.205 13.131 2.636 7.397
(0.969) (0.969) (0.457) (0.995) (0.216) (0.989) (0.688)
Jump Ratio 41.67% 26.67% 35.00% 35.00% 23.33% 35.00% 35.00%
Note: 1. *, **, and *** are significant at 10, 5, and 1%, respectively
2.Q(10) The verification statistics using the Ljung-Box Q test are used to verify the self-correlation of the
normalized time interval. The value in the parentheses is the P value of the test, and the value in the brackets
is the standard error of the estimated parameter.
3. Jump ratio is the number of jumps frequency divided by the number of days.
37 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
Table 8 FinTech ETF, Financial ETF and Technology ETF of Asymmetric Integration table
Panel ETF
code ARMA GARCH
EGARCH GJR GARCH
Jump
percentage
Jump
Average
percentage ARMA/
GARCH Result
Leverage
effect
ARMA/
GARCH Result
Leverage
effect
Panel A
FinTech
ARKW (0,0) (2,1) (0,0)/
(2,1) -*** YES
(0,0)/
(2,1) NO NO 16.67%
24.76%
BOTZ (2,3) (1,1) (2,3)/
(1,1) -*** YES
(2,3)/
(1,1) NO NO 31.67%
EMQQ (2,2) (2,2) (2,2)/
(2,2) -* YES
(2,2)/
(2,2) NO NO 21.67%
FINX (3,2) (0,1) (3,2)/
(0,1) -*** YES
(3,2)/
(0,1) +* YES 30.00%
IPAY (2,3) (0,1) (2,3)/
(1,1) -*** YES
(2,3)/
(1,1) +*** NO 30.00%
SKYY (2,2) (1,1) (2,2)/
(1,1) -*** YES
(2,2)/
(1,1) +*** NO 31.67%
SNSR (2,1) (1,1) (2,1)/
(1,1) -*** YES
(2,1)/
(1,1) +*** NO 11.67%
Panel B
Financial
FAS (2,2) (2,2) (2,2)/
(2,2) -*** YES
(2,2)/
(2,2) NO NO 33.33%
28.81%
FNCL (2,2) (1,1) (2,2)/
(1,1) -*** YES
(2,2)/
(1,1) +* YES 28.33%
KBE (3,2) (2,1) (3,2)/
(2,1) -*** YES
(3,2)/
(2,1) NO NO 13.33%
FXO (2,2) (1,1) (2,2)/
(1,1) -*** YES
(2,2)/
(1,1) +** YES 30.00%
KIE (3,3) (2,2) (3,3)/
(2,2) -*** YES
(3,3)/
(2,1) +*** YES 26.67%
PSK (1,0) (1,1) (1,0)/
(1,1) -*** YES
(1,0)/
(1,1) NO NO 40.00%
XLF (2,2) (1,2) (2,2)/
(1,2) -*** YES
(2,2)/
(1,2) +* YES 30.00%
Panel C
Technology
IGM (2,2) (2,2) (2,2)/
(2,2) -*** YES
(2,2)/
(0,1) NO NO 41.67%
33.10%
IGV (3,3) (2,1) (3,3)/
(2,1) -*** YES
(3,3)/
(1,1) +** NO 26.67%
IXN (2,2) (1,1) (2,2)/
(1,1) -*** YES
(2,2)/
(1,1) +*** NO 35.00%
IYW (2,2) (2,2) (2,2)/
(2,2) -*** YES
(2,2)/
(2,2) +*** NO 35.00%
SMH (2,2) (1,1) (2,2)/
(1,1) -*** YES
(2,2)/
(1,1) NO NO 23.33%
VGT (2,2) (1,1) (2,2)/
(1,1) -*** YES
(2,2)/
(1,1) +*** NO 35.00%
XLK (2,3) (1,1) (2,3)/
(1,1) -*** YES
(2,3)/
(0,1) +** YES 35.00%
Note: 1. *, **, and *** are significant at 10, 5, and 1%, respectively.
2. "-" is negative and "+" is positive.
38 Chen and Tung, Journal of International and Global Economic Studies, 12(2), December 2019, 19-41
5. Conclusions and Suggestions
This paper examined the empirical research on the asymmetric effect of FinTech, Financial,
and Technology ETFs. First, the study used the ARMA model to find the category that best fits
the ARCH effect and then found the results of GARCH. Moreover, EGARCH, GJR GARCH,
and jump GARCH models are used for examining asymmetry related to price fluctuations.
The empirical results of EGARCH showed that the influence of bad news in each group
was better than the good news. In order to improve the prediction performance, the result of
GJR GARCH satisfies the condition which the fluctuation caused by the negative accidental
shock was greater than the fluctuation caused by the expected shock. The Financial ETFs were
the best performance of GJR GARCH. The jump effect satisfies the conditional discrete
fluctuation variance, indicating the discontinuity of the fluctuation. The Technology ETFs were
the best for jump effect, while Technology and Financial ETFs have the best volatility
asymmetry due to developing for a long time. Many emerging FinTech stocks have been
invested and received public attention since 2015. FinTech ETFs still needs to continue to
develop for a while, so return volatility still has no complete trend.
The results found that Financial and Technology ETFs have asymmetric and leverage
effects compared with FinTech ETFs. Bad news in both markets will be greater than good news.
The Technology ETF market existed on the effect of discrete jumps. Thus, investors can use
discrete jumps to reduce investment losses. Although FinTech ETFs have relatedly weak
performance effect than Financial and Technology ETFs, leverage and discrete jump effects are
quite helpful in reducing the loss of investment strategies.
Endnotes
Jo-Hui Chen, Email: [email protected].
Chia-Shan Tung, Email: [email protected].
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