• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.443-455
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• 2017

In this paper, we study ARCH(${\infty}$) models with either geometrically decaying coefficients or hyperbolically decaying coefficients. Most popular autoregressive conditional heteroscedasticity (ARCH)-type models such as various modified generalized ARCH (GARCH) (p, q), fractionally integrated GARCH (FIGARCH), and hyperbolic GARCH (HYGARCH). can be expressed as one of these cases. Sufficient conditions for $L_2$-near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(${\infty}$) models are proved.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.783-791
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• 2004

In this paper we review recent developments in nonlinear time series modeling on both conditional mean and conditional variance. Traditional linear model in conditional mean is referred to as ARMA(autoregressive moving average) process investigated by Box and Jenkins(1976). Nonlinear mean models such as threshold, exponential and random coefficient models are reviewed and their characteristics are explained. In terms of conditional variances, ARCH(autoregressive conditional heteroscedasticity) class is considered as typical linear models. As nonlinear variants of ARCH, diverse nonlinear models appearing in recent literature including threshold ARCH, beta-ARCH and Box-Cox ARCH models are remarked. Also, a class of unified nonlinear models are considered and parameter estimation for that class is briefly discussed.

• Journal of Technologic Dentistry
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• v.35 no.1
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• pp.29-35
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• 2013

Purpose: The purpose of this study was to evaluate the validity of digital models fabricated by dental scannable stone. Methods: Twenty same cases of stone models(maxillary full arch) were manufactured. Intercanine distance, intermolar distance, two dental arch lengths(right, left), two diagonal of dental arch lengths(right, left) were measured for comparison. Each of ten stone models were measured by digital vernier calipers and scanned by dental scanner. Ten digital models were measured by CAD program. The mean(SDs) values were compared by a Mann-Whitney U test(${\alpha}$=0.05). Results: No statistically significant differences between the two groups were found at intermolar distance, dental arch length(right)(p>0.05). However, intercanine distance, dental arch length(left) and two diagonal of dental arch lengths(right, left) were statistically significant(p<0.05). Conclusion: Stone models fabricated by dental scannable stone showed larger than digital models.

• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.33-40
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• 2005

The estimating function method was proposed by Godambe(1985) for parameter estimation under unknown distributions for errors in the models. Threshold Autoregressive Heteroscedastic (Threshold-ARCH) models have been developed by Zakoian(1994) and Li and Li(1996) for explaining the asymmetric properties in the financial time series data. In this paper, we apply the estimating function method to the Threshold-ARCH model and show that the proposed estimators perform better than the MLE under the heavy-tailed distributions.

• The korean journal of orthodontics
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• v.45 no.2
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• pp.74-81
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• 2015

Objective: The purposes of this study were 1) to classify lingual dental arch form types based on the lingual bracket points and 2) to provide a new lingual arch form template based on this classification for clinical application through the analysis of three-dimensional virtual models of normal occlusion sample. Methods: Maxillary and mandibular casts of 115 young adults with normal occlusion were scanned in their occluded positions and lingual bracket points were digitized on the virtual models by using Rapidform 2006 software. Sixty-eight cases (dataset 1) were used in K-means cluster analysis to classify arch forms with intercanine, interpremolar and intermolar widths and width/depth ratios as determinants. The best-fit curves of the mean arch forms were generated. The remaining cases (dataset 2) were mapped into the obtained clusters and a multivariate test was performed to assess the differences between the clusters. Results: Four-cluster classification demonstrated maximum inter-cluster distance. Wide, narrow, tapering, and ovoid types were described according to the intercanine and intermolar widths and their best-fit curves were depicted. No significant differences in arch depths existed among the clusters. Strong to moderate correlations were found between maxillary and mandibular arch widths. Conclusions: Lingual arch forms have been classified into 4 types based on their anterior and posterior dimensions. A template of the 4 arch forms has been depicted. Three-dimensional analysis of the lingual bracket points provides more accurate identification of arch form and, consequently, archwire selection.

• The korean journal of orthodontics
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• v.20 no.1
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• pp.183-195
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• 1990

The purposes of present study were to identify possible relationships between post-treatment changes and post-retention changes. The patient's models were composed of 58 samples, and were classified non-extraction group (30 samples) and extraction group (28 samples). For each sample the first models were taken prior to the start of treatment, the second models just after the end of treatment, and the third models two years after. The results were as follows: 1. In the cases of non-extraction group, increases were in intermolar width of maxilla, interbicuspid width of maxilla and arch perimeter of mandible during treatment period, but decreases were in the same measurements during post-retention period. 2. In the cases of extraction group, decreases were in intermolar width of mandible, interbicuspid widths of maxilla and mandible, arch length of mandible, arch perimeters of maxilla and mandible during treatment period. 3. Significant decreases were in the irregularity index of both extraction and non-extraction group during treatment period. 4. There were significant differences of arch dimensional changes in intermolar widths of maxilla and mandible, interbicuspid widths of maxilla and mandible, arch lengths of maxilla and mandible, arch perimeters of maxilla and mandible between non-extraction and extraction group.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.983-991
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• 2017

High frequency time series are now prevalent in financial data. However, models need to be further developed to suit high frequency time series that account for intraday volatilities since traditional volatility models such as ARCH and GARCH are concerned only with daily volatilities. Due to $H{\ddot{o}}rmann$ et al. (2013), functional ARCH abbreviated as fARCH is proposed to analyze intraday volatilities based on high frequency time series. This article introduces fARCH to readers that illustrate intraday volatility configuration on the KOSPI and the Hyundai motor company based on the data with one minute high frequency.

• Journal of the Korean Statistical Society
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• v.34 no.1
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• pp.61-71
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• 2005

A class of asymmetric ARCH processes is proposed via binary random power transformations. This class accommodates traditional nonlinear models such as threshold ARCH (Rabemanjara and Zacoian (1993)) and Box-Cox type ARCH models(Higgins and Bera (1992)). Stationarity condition of the model is addressed. Iterative least squares(ILS) and pseudo maximum like-lihood(PML) methods are discussed for estimating parameters and related algorithms are presented. Illustrative analysis for Korea Stock Prices Index (KOSPI) data is conducted.

• The korean journal of orthodontics
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• v.43 no.6
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• pp.288-293
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• 2013

Objective: This study was aimed at comparing the mandibular arch forms of Korean and Vietnamese patients by using facial axis (FA) points on three-dimensional (3D) models. Methods: Mandibular casts of 68 Korean (Class I malocclusion, 30; Class II malocclusion, 38) and 78 Vietnamese (Class I malocclusion, 41; Class II malocclusion, 37) patients were scanned in their occluded positions and grouped according to arch form (tapered, ovoid, and square). The FA point of each tooth was digitized on the 3D mandibular models. The measurements and frequency distributions of the arch forms were compared between the ethnic groups. Results: The Vietnamese patients had significantly greater intercanine depth and intercanine and intermolar width-to-depth ratios than the Korean patients (p < 0.05). The frequency distributions of the arch forms were also significantly different (p = 0.038), but no sexual dimorphism was found. Conclusions: Vietnamese people tend to have deeper and wider arches than Korean people. The three arch forms are evenly distributed in Korean people, but Vietnamese people frequently have square arches. Clinicians should identify the correct arch form of an ethnic group before initiating orthodontic treatment.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.495-504
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• 2001

In this paper we consider the (generalized) autoregressive model with conditional heteroscedasticity (ARCH/GARCH models). We willing give conditions under which strict stationarity, ergodicity and the functional central limit theorem hold for the corresponding models.