• The Journal of Asian Finance, Economics and Business
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• v.7 no.12
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• pp.1-10
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• 2020

This study investigates the problem of outlier detection based on discrete wavelet transform in the context of time series data where the identification and treatment of outliers constitute an important component. An outlier is defined as a data point that deviates so much from the rest of observations within a data sample. In this work we focus on the application of the traditional method suggested by Tukey (1977) for detecting outliers in the closed price series of the Saudi Arabia stock market (Tadawul) between Oct. 2011 and Dec. 2019. The method is applied to the details obtained from the MODWT (Maximal-Overlap Discrete Wavelet Transform) of the original series. The result show that the suggested methodology was successful in detecting all of the outliers in the series. The findings of this study suggest that we can model and forecast the volatility of returns from the reconstructed series without outliers using GARCH models. The estimated GARCH volatility model was compared to other asymmetric GARCH models using standard forecast error metrics. It is found that the performance of the standard GARCH model were as good as that of the gjrGARCH model over the out-of-sample forecasts for returns among other GARCH specifications.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.4
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• pp.59-70
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• 2020

The purpose of this study is to construct the ACD model for the block trading volume duration. The ACD model based on the block trading volume duration is referred to as Volume ACD (VACD) in this study. By integrating with GARCH-type models, the VACD based GARCH type models, which include VACD-GARCH, VACD-IGARCH and VACD-FIGARCH models, are set up. This study selects Chunghwa Telecom (CHT) Inc., offering the America Depository Receipt (ADR) in NYSE, to investigate the block trading volume duration in Taiwanese equity market. The empirical results indicate that the long memory in volume duration series increases dependence at level of volatility clustering by VACD (2,1)-FIGARCH (3,d,1) model. Moreover, the VACD (2,1)-IGARCH (1,1) exhibits relatively better performance of prediction on capturing block trading volume duration. This volatility model is more appropriate in this study to portray the change of the CHT Inc. prices and provides more information about the volatility process for investment strategy, which can be a reference indicator of financial asset pricing, hedging strategy and risk management.

• Journal of Intelligence and Information Systems
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• v.23 no.2
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• pp.107-122
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• 2017

Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.

• Journal of Korea Port Economic Association
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• v.31 no.1
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• pp.1-14
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• 2015

The standard GARCH model imposing symmetry on the conditional variance, tends to fail in capturing some important features of the data. This paper, hence, introduces the models capturing asymmetric effect. They are the EGARCH model and the GJR model. We provide the systematic comparison of volatility models focusing on the asymmetric effect of news on volatility. Specifically, three diagnostic tests are provided: the sign bias test, the negative size bias test, and the positive size bias test. This paper shows that there is significant evidence of GARCH-type process in the data, as shown by the test for the Ljung-Box Q statistic on the squared residual data. The estimated unconditional density function for squared residual is clearly skewed to the left and markedly leptokurtic when compared with the standard normal distribution. The observation of volatility clustering is also clearly reinforced by the plot of the squared value of residuals of export volume and values. The unconditional variance of both export volumes and export value indicates that large shocks of either sign tend to be followed by large shocks, and small shocks of either sign tend to follow small shocks. The estimated export volume news impact curve for the GARCH also suggests that $h_t$ is overestimated for large negative and positive shocks. The conditional variance equation of the GARCH model for export volumes contains two parameters ${\alpha}$ and ${\beta}$ that are insignificant, indicating that the GARCH model is a poor characterization of the conditional variance of export volumes. The conditional variance equation of the EGARCH model for export value, however, shows a positive sign of parameter ${\delta}$, which is contrary to our expectation, while the GJR model exhibits that parameters ${\alpha}$ and ${\beta}$ are insignificant, and ${\delta}$ is marginally significant. That indicates that the asymmetric volatility models are poor characterization of the conditional variance of export value. It is concluded that the asymmetric EGARCH and GJR model are appropriate in explaining the volatility of export volume, while the symmetric standard GARCH model is good for capturing the volatility.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.495-506
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• 2015

Volatility is a variation measure in finance for returns of a financial instrument over time. GARCH models have been a popular tool to analyze volatility of financial time series data since Bollerslev (1986) and it is said that volatility is highly persistent when the sum of the estimated coefficients of the squared lagged returns and the lagged conditional variance terms in GARCH models is close to 1. Regarding persistence, numerous methods have been proposed to test if such persistency is due to volatility shifts in the market or natural fluctuation explained by stationary long-range dependence (LRD). Recently, Lee et al. (2015) proposed a residual-based cumulative sum (CUSUM) test statistic to test volatility shifts in GARCH models against LRD. We propose a bootstrap-based approach for the residual-based test and compare the sizes and powers of our bootstrap-based CUSUM test with the one in Lee et al. (2015) through simulation studies.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.395-404
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• 2013

This paper studies the skewness of the absolute value GARCH(1, 1) models with Gaussian mixture innovations (Gaussian mixture AVGARCH(1, 1) models). The maximum estimated-likelihood estimator (MELE) employed (a two- step estimation method in order to estimate the skewness of Gaussian mixture AVGARCH(1, 1) models. Through the real data analysis, the adequacy of adopting Gaussian mixture innovations is exhibited in reflecting the skewness of two major Korean stock indices.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.237-245
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• 2007

Nonlinear asymmetric time series models have the growing interest in econometrics and finance. Threshold model is one of the successful asymmetric model. We consider a smooth transition ARMA model which converges a.s. to a threshold ARMA model and show that the smooth transition ARMA model admits a stationary measure, provided a suitable condition on the coefficients of the autoregressive parts of the different regimes is satisfied. Stationarity of a smooth transition GARCH model is also obtained.

• Journal of Information Technology Applications and Management
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• v.26 no.6
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• pp.47-63
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• 2019

The volatility of major crypto currencies was examined and they are diagnosed whether they have a systematic risk or not, by estimating market beta representing systematic risk using GARCH( Generalized Auto Regressive Conditional Heteroskedastieity) model. First, the empirical results showed that their prices are very volatile over time because of the existence of ARCH and GARCH effects. Second, in terms of efficiency, asymmetric GJR model was estimated to be the most appropriate model because the standard error of a market beta was less than that of the OLS model and GARCH model. Third, the estimated market beta of Bitcoin using GJR model was less than 1 at 0.8791, showing that there is no systematic risk. However, unlike OLS model, the market beta of Ethereum and Ripple was estimated at 1.0581 and 1.1222, showing that there is systematic risk. This result shows that bitcoin is less dangerous than Ripple and Ethereum, and ripple is the most dangerous of all three crypto currencies. Finally, the major cryptocurrency found that the negative impact caused greater variability than the positive impact, causing bad news to fluctuate more than good news, and therefore good news and bad news had a different effect on the variability.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.49-61
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• 2010

The time series dependencies of Financial volatility are frequently measured by the autocorrelation function of power-transformed absolute returns. It is known as the Taylor property that the autocorrelations of the absolute returns are larger than those of the squared returns. Hass (2009) developed a simple method for detecting the Taylor property in absolute-value-GAROH(1,1) (AVGAROH(1,1)) model. In this article, we fitted AVGAROH(1,1) model for various Korean financial time series and observed the Taylor property.

• The Korean Journal of Financial Management
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• v.20 no.1
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• pp.305-329
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• 2003

This work analyzes the influence of the dollar and yen currency on the rate of return of the individual firms and its symmetries based on the data from Jan. 5 1987 to Dec. 28, 2001. GARCH and autoregressive error models were used for on the daily data, due to the heteroscedascity and autoregression of the error terms, and as for the monthly data, this paper follows the autoregressive error models. Daily data fumed out to be a better explanatory variable in detecting exchange rate exposure, and EGARCH(1, 1) and GJR-GRARCH(1, 1) have higher competence in analyzing the daily data. Also, most of the exposed firms have been exposed in the negative region, and appreciation of exchange rate does not help enhancing the asset value of the domestic value. Analysis on the asymmetries let us conclude that high proportion of domestic firms face asymmetric exchange rate exposure, and that the pricing-to-market theory carries more conviction than the real option theory. Furthermore, monthly data are more precise in analysis of asymmetries.