• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.463-475
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• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.453-458
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• 2009

In this paper, we consider Jarque-Bera (JB) normality test for the innovations of ARMA-GARCH models. In financial applications, JB test based on the residuals are routinely used for the normality of ARMA-GARCH innovations without a justification. However, the validity of JB test should be justified in advance of the actual practice (Lee et al., 2009). Through the simulation study, it is found that the validity of JB test depends on the shape of test statistic. Specifically, when the constant term is involved in ARMA model, a certain type of residual based JB test produces severe size distortions.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.423-435
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• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.809-815
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• 2007

Since Bollerslev(1986), the GARCH model has been popular in analysing the volatility of the financial time series. In real data analysis, practitioners conventionally put the normal assumption on the innovation random variables of the GARCH model, which is often violated. In this paper, we analyse the domestic financial data based on the GARCH(1,1) model and among existing normality tests, perform the Jarque-Bera test based on the residuals. It is shown that the innovation based on the GARCH(1,1) model dose not follow the normality assumption.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1399-1412
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• 2016

We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.

• Journal of Korea Water Resources Association
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• v.39 no.12 s.173
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• pp.997-1012
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• 2006

We have presented a nonparametric stochastic approach for the SOI(Southern Oscillation Index) series that used nonlinear methodology called Nonlinear AutoRegressive(NAR) based on conditional kernel density function and CAFPE(Corrected Asymptotic Final Prediction Error) lag selection. The fitted linear AR model represents heteroscedasticity, and besides, a BDS(Brock - Dechert - Sheinkman) statistics is rejected. Hence, we applied NAR model to the SOI series. We can identify the lags 1, 2 and 4 are appropriate one, and estimated conditional mean function. There is no autocorrelation of residuals in the Portmanteau Test. However, the null hypothesis of normality and no heteroscedasticity is rejected in the Jarque-Bera Test and ARCH-LM Test, respectively. Moreover, the lag selection for conditional standard deviation function with CAFPE provides lags 3, 8 and 9. As the results of conditional standard deviation analysis, all I.I.D assumptions of the residuals are accepted. Particularly, the BDS statistics is accepted at the 95% and 99% significance level. Finally, we split the SOI set into a sample for estimating themodel and a sample for out-of-sample prediction, that is, we conduct the one-step ahead forecasts for the last 97 values (15%). The NAR model shows a MSEP of 0.5464 that is 7% lower than those of the linear model. Hence, the relevance of the NAR model may be proved in these results, and the nonparametric NAR model is encouraging rather than a linear one to reflect the nonlinearity of SOI series.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.6
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• pp.212-217
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• 2020

The purpose of this study was to analyze the volatility and properties of a time series for tangerine prices in Jeju using the GARCH model of Bollerslev(1986). First, it was found that the time series for the rate of change in tangerine prices had a thicker tail rather than a normal distribution. At a significance level of 1%, the Jarque-Bera statistic led to a rejection of the null hypothesis that the distribution of the time series for the rate of change in tangerine prices is normally distributed. Second, the correlation between the time series was high based on the Ljung-Box Q statistic, which was statistically verified through the ARCH-LM test. Third, the results of the GARCH(1,1) model estimation showed statistically significant results at a significance level of 1%, except for the constant of the mean equation. The persistence parameter value of the variance equation was estimated to be close to 1, which means that there is a high possibility that a similar level of volatility will be present in the future. Finally, it is expected that the results of this study can be used as basic data to optimize the government's tangerine supply and demand control policy.

• The Journal of Fisheries Business Administration
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• v.40 no.2
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• pp.49-70
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• 2009

This study proviedes GARCH model(Bollerslev, 1986) to analyze the structural characteristics of price volatility in domestic aquacultural fish market of Korea. As a case study, flatfish and rock-fish are analyzed as major species with relatively high portion in an aspect of production volume among fish captured in Korea. For analyzing, this study uses daily market data (dating from Jan 1 2000 to June 30, 2008) published by the Noryangjin Fisheries Wholesale Market which is located in Seoul of Korea. This study performs normality test on trading volume and price volatility of flatfish and rock-fish as an advanced empirical approach. The normality test adopted is Jarque-Bera test statistic. As a result, first, a null hypothesis that "an empirical distribution follows normal distribution" was rejected in both fishes. The distribution of daily market data of them were not only biased toward positive(+) direction in terms of kurtosis and skewness, but also characterized by leptokurtic distribution with long right tail. Secondly, serial correlations were found in data on market trading volume and price volatility of two species during very long period. Thirdly, the results of unit root test and ARCH-LM test showed that all data of time series were very stationary and demonstrated effects of ARCH. These statistical characteristics can be explained as a reasonable ground for supporting the fitness of GARCH model in order to estimate conditional variances that reveal price volatility in empirical analysis. From empirical data analysis above, this study drew the following conclusions. First of all, from an empirical analysis on potential effects of seasonality and the day of week on price volatility of aquacultural fish, Monday effects were found in both species and Thursday and Friday effects were also found in flatfish. This indicates that Monday is effective in expanding price volatility of aquacultural fish market and also Monday has higher effects upon the price volatility of fish than other days of week have since it has more new information for weekend. Secondly, the empirical analysis led to a common conclusion that there was very high price volatility of flatfish and rock-fish. This points out that the persistency parameter($\lambda$), an index of possibility for current volatility to sustain similarly in the future, was higher than 0.8-equivalently nearly to 1-in both flatfish and rock-fish, which presents volatility clustering. Also, this study estimated and compared and model that hypothesized normal distributions in order to determine fitness of respective models. As a result, the fitness of GARCH(1, 1)-t model was better than model where the distribution of error term was hypothesized through-distribution due to characteristics of fat-tailed distribution, was also better than model, as described in the results of basic statistic analysis. In conclusion, this study has an important mean in that it was introduced firstly in Korea to investigate in price volatility of Korean aquacultural fishery products, although there was partially a limited of official statistic data. Therefore, it is expected that the results of this study will be useful as a reference material for making and assessing governmental policies. Also, it is looked forward that the results will be helpful to build a fishery business plan as and aspect of producer, and also to take timely measures to potential price fluctuations of fishery products in market. Hence, it is advisable that further studies related to such price volatility in fishery market will extend and evolve into a wider variety of articles and issues in near future.