the empirical study of volatility asymmetry for fintech etf dec 201… · lin (2014) explored the...

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.

https://www.cmoney.tw/notes/note-detail.aspx?nid=166310


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


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.


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


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:

http://www.moneydj.com/


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


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.


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


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.


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.


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.


Table 3 FinTech ETF, Financial ETF and Technology ETF - Summary Statistics of Unit Root,

LM, and ARMA-LM Testing for ETF and Index Returns



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)



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)



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.


Table 4 ARMA-GARCH of FinTech ETF, Financial ETF and Technology ETF

Part A: FinTech ETF


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


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


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.


Table 5 EGARCH-ARMA of FinTech ETF, Financial ETF and Technology ETF

Part A: FinTech ETF


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


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


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.


Table 6 GJR GARCH of FinTech ETF, Financial ETF and Technology ETF



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



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



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.


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.


Table 7 Realized Jump (RJ) GARCH of Descriptive Statistics


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%


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%


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.


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.


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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