• 대한수학회보
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• 제52권4호
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• pp.1047-1057
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• 2015

In [6], it is proved that the lengths of periods occurring in the ${\beta}$-expansion of a rational series r noted by $Per_{\beta}(r)$ depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic ${\beta}$-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if $r=\frac{P}{Q}$ is written in reduced form with |P| < |Q|, we will generalize the curious property "$Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$".

• 대한수학회지
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• 제42권5호
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• pp.1003-1015
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• 2005

Klein proved that polynomial rings over nil rings of bounded index are also nil of bounded index; while Puczylowski and Smoktunowicz described the nilradical of a power series ring with an indeterminate. We extend these results to those with any set of commuting indeterminates. We also study prime radicals of power series rings over some class of rings containing the case of bounded index, finding some examples which elaborate our arguments; and we prove that R is a PI ring of bounded index then the power series ring R[[X]], with X any set of indeterminates over R, is also a PI ring of bounded index, obtaining the Klein's result for polynomial rings as a corollary.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권5호
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• pp.233-240
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• 2001

This paper presents a time series prediction method using a fuzzy rule-based system. Extracting fuzzy rules by performing a simple one-pass operation on the training data is quite attractive because it is easy to understand, verify, and extend. The simplest method is probably to relate an estimate, x(n+k), with past data such as x(n), x(n-1), ..x(n-m), where k and m are prefixed positive integers. The relation is represented by fuzzy if-then rules, where the past data stand for premise part and the predicted value for consequence part. However, a serious problem of the method is that it cannot handle nonstationary data whose long-term mean is varying. To cope with this, a new training method is proposed, which utilizes the difference of consecutive data in a time series. In this paper, typical previous works relating time series prediction are briefly surveyed and a new method is proposed to overcome the difficulty of prediction nonstationary data. Finally, computer simulations are illustrated to show the improved results for various time series.

• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.453-458
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• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• 한국환경과학회지
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• 제8권3호
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• pp.349-354
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• 1999

The transfer function was introduced to establish the prediction method for the DO concentration at the intaking point of Kongju Water Works System. In the mose cases we analyze a single time series without explicitly using information contained in the related time series. In many forecasting situations, other events will systematically influence the series to be forecasted(the dependent variables), and therefore, there is need to go beyond a univariate forecasting model. Thus, we must bulid a forecasting model that incorporates more than one time series and introduces explicitly the dynamic characteristics of the system. Such a model is called a multiple time series model or transfer function model. The purpose of this study is to develop the stochastic stream water quality model for the intaking station of Kongju city waterworks in Keum river system. The performance of the multiplicative ARIMA model and the transfer function noise model were examined through comparisons between the historical and generated monthly dissolved oxygen series. The result reveal that the transfer function noise model lead to the improved accuracy.

• 응용통계연구
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• 제20권2호
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• pp.219-227
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• 2007

시계열 모형은 통신망 트래픽의 예측과 분석에 유용하게 쓰여 왔다. 본 논문에서는 통신망 트래픽의 예측을 위하여 다양한 시계열 모형을 소개하고 성능평가를 하고자 한다. 이를 위하여 실제 통신망 트래픽 자료에 선형 및 비선형 시계열모형을 적합 시키고 비선형 시계열모형이 선형 시계열 모형보다 예측의 정확도가 우수함을 보이고자 한다.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.91-109
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• 1995

The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.657-666
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• 2002

ThE Gibbs' phenomenon in the classical Fourier series is well-known. It is closely related with the kernel of the partial sum of the series. In fact, the Dirichlet kernel of the courier series is not positive. The poisson kernel of Cesaro summability is positive. As the consequence of the positiveness, the partial sum of Cesaro summability does not exhibit the Gibbs' phenomenon. Most kernels associated with wavelet expansions are not positive. So wavelet series is not free from the Gibbs' phenomenon. Because of the excessive oscillation of wavelets, we can not follow the techniques of the courier series to get rid of the unwanted quirk. Here we make a positive kernel For Meyer wavelets and as the result the associated summability method does not exhibit Gibbs' phenomenon for the corresponding series .

• 한국수학사학회지
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• 제23권1호
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• pp.53-66
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• 2010

본 논문에서는 푸리에 급수의 $L^1$-수렴성에 대한 20세기 초부터 중반(W. H. Young부터 G. A. Fomin)까지 고전적인 연구 결과를 고찰하고 연구자들의 소계보를 조사한다. 푸리에 급수 부분합의 수렴성 문제를 동치관계인 푸리에 계수 성질을 이용하여 수렴성을 보인 결론들의 상호 연계성을 재해석한다.

• Journal of the Korean Data and Information Science Society
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• 제18권1호
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• pp.73-80
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• 2007

Cointegration(together with VARMA(vector ARMA)) has been proven to be useful for analyzing multivariate non-stationary data in the field of financial time series. It provides a linear combination (which turns out to be stationary series) of non-stationary component series. This linear combination equation is referred to as long term equilibrium between the component series. We consider two sets of Korean bivariate financial time series and then illustrate cointegration analysis. Specifically estimated VAR(vector AR) and VECM(vector error correction model) are obtained and CV(cointegrating vector) is found for each data sets.