• Communications for Statistical Applications and Methods
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• v.30 no.2
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• pp.149-162
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• 2023

The ℓ₁-trend filtering method is one of the most widely used methods for extracting underlying trends from noisy observations. Contrary to the Hodrick-Prescott filtering, the ℓ₁-trend filtering gives piecewise linear trends. One of the advantages of the ℓ₁-trend filtering is that it can be used for identifying change points in piecewise linear trends. However, since the ℓ₁-trend filtering employs total variation as a penalty term, estimated piecewise linear trends tend to be biased. In this study, we demonstrate the biasedness of the ℓ₁-trend filtering in trend level estimation and propose a two-stage bias-reduction procedure. The newly suggested estimator is based on the estimated change points of the ℓ₁-trend filtering. Numerical examples illustrate that the proposed method yields less biased estimates for piecewise linear trends.

• Industrial Engineering and Management Systems
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• v.8 no.4
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• pp.257-263
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• 2009

Focusing on the idea that the equation of exponential smoothing method (ESM) is equivalent to (1, 1) order ARMA model equation, new method of estimation of smoothing constant in exponential smoothing method is proposed before by us which satisfies minimum variance of forecasting error. Theoretical solution was derived in a simple way. Mere application of ESM does not make good forecasting accuracy for the time series which has non-linear trend and/or trend by month. A new method to cope with this issue is required. In this paper, combining the trend removal method with this method, we aim to improve forecasting accuracy. An approach to this method is executed in the following method. Trend removal by a linear function is applied to the original shipping data of consumer goods. The combination of linear and non-linear function is also introduced in trend removal. For the comparison, monthly trend is removed after that. Theoretical solution of smoothing constant of ESM is calculated for both of the monthly trend removing data and the non monthly trend removing data. Then forecasting is executed on these data. The new method shows that it is useful especially for the time series that has stable characteristics and has rather strong seasonal trend and also the case that has non-linear trend. The effectiveness of this method should be examined in various cases.

• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.455-471
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• 2000

A new method is developed for estimating the mean of a population which has a linear trend. The proposed estimator is based on the balanced systematic sampling method and the concept of interpolation. The efficiency of the proposed method is compared with that of existing methods.

• The Korean Journal of Applied Statistics
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• v.36 no.6
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• pp.573-589
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• 2023

In a piecewise linear trend model, the change points coincide with the mean change points of the first differenced time series. Therefore, by detecting the mean change points of the first differenced time series, one can estimate the change points of the piecewise linear trend model. In this paper, based on this fact, a method is proposed for detecting change points of the piecewise linear trend model using the simple moving average of the first differenced time series rather than estimates of the slope or residuals. Our Monte Carlo simulation experiments show that the proposed method performs well in estimating the number of change points not only when the error terms in the piecewise linear trend model are independent but also when they are serially correlated.

• Ocean and Polar Research
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• v.28 no.4
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• pp.415-423
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• 2006

Interannual variation and long-term trends of coastal sea surface temperature (SST) in Korea were investigated by analyzing 27 coastal SST time series from 1969 to 2004. Long-term linear increasing trend was remarkable with the rate over $0.02^{\circ}C/year$ at almost all the stations. The slope of long-term linear trend was larger at the stations along the eastern coast than in the western and southern regions. It was also noticeable that there was a common tendency of interannual variability with the period of 3-5 years at most of the stations. SST was lower in the 1970's and early 1980's while it was higher in the 1990's and early 2000's after the increase in the late 1980's. The pattern of the interannual variability of SST was similar to that of air temperature. Increasing trend of minimum SST in winter was obvious at most stations na it was larger along the eastern coast, while the linear trend of maximum SST in summer was less definite. Therefore, the decreasing tendency of annual amplitude was mainly due to the increasing tendency of SST in winter.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.365-379
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• 2002

We apply the techniques of interpolation and extrapolation to derive a new estimator based on centered modified systematic sampling for the mean of a population which has a linear trend. The efficiency of the proposed estimation method is compared with that of various existing methods. An illustrative numerical example is given.

• The Korean Journal of Applied Statistics
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• v.10 no.1
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• pp.163-175
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• 1997

Randomization of the run order within a block is a technique commonly employed by the experimenters of block designs to avoid biases in the estimates of the effects of interest. In practice, however the experimental responses are sometimes affected by the spatial or temporal position of the experimental units within a block. In such cases, it is preferable to use a systematic ordering of the treatments. It is often possible to find an ordering which will allow the estimation of treatment effects independently of any trend is known as a trend-free block designs. In many idustrial and agricultural experiments, treatments are applied to experimental units sequentially in time or space. This paper begins with a review of concepts and properties of trend-free designs. We, then devise algorithms to generate linear trend-free designs. We extend and modify the existing algorithm which is given by Bradley and Odeh(1988). Also, the algorithm which generate all possible linear trend-free designs in provided.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.1-12
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• 2004

In this paper, Yates' end corrections method is centralized to estimate the mean of a population which has a linear trend in the case of k (the reciprocal of the sampling fraction) even. The efficiency of the resultant method is compared with that of existing methods.

• International Journal of Advanced Culture Technology
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• v.4 no.3
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• pp.24-38
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• 2016

The purpose of our study is to analyze the effect of socio-economic status on the diet pattern of Korean adults. Raw data from the fifth (2010-2012) Korea National Health and Nutrition Examination Survey (KNHANES) were used, and finally 11,700 adults were analyzed as subjects. Results in consideration of the socio-economic status of the subjects, a linear trend was observed in men in which the odds ratio of having lunch (p for trend=0.006) and dinner (p for trend=0.0317) decreased as the level of education went down. In diet frequency, a decreasing trend (p for trend=0.0328) was observed in which the odds ratio of having 3 meals a day reduced as the household income lowered. For women, a linear trend (p for trend=0.0012) was observed in which the frequency of dinner decreased as the level of education became lower. A falling trend in the rate of having 3 meals a day was also observed (p for trend=0.0135). Our study analyzed the characteristics of the diet patterns of individuals according to their socio-economic status with the purpose of suggesting guidelines for correcting. To prevent this, we will need education and awareness and public attention for the practice of correct eating habits.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.21 no.2
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• pp.67-77
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• 2016

This study developed synthetic regression diagram for analyzing the linear trend of sea surface height, temperature, and salinity around the Korean marginal seas. In situ observed data had been quality controlled and they were verified by EOF comparison with objective analyzed data. From the synthetic regression diagram, we confirmed similar linear regression values with those of previous studies, but additionally provided detailed regression rate of each 5 to 30 year for the total periods of 1983-2013. We expect that quantitative results presented by this study will be useful as standard reference numbers for relevant studies analyzing oceanic long-term trend.