• Title/Summary/Keyword: FARIMA

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ON THE CONVERGENCE OF FARIMA SEQUENCE TO FRACTIONAL GAUSSIAN NOISE

  • Kim, Joo-Mok
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.2
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    • pp.411-420
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    • 2013
  • We consider fractional Gussian noise and FARIMA sequence with Gaussian innovations and show that the suitably scaled distributions of the FARIMA sequences converge to fractional Gaussian noise in the sense of finite dimensional distributions. Finally, we figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, $d$, 0) by using R/S method.

PARAMETER ESTIMATION AND SPECTRUM OF FRACTIONAL ARIMA PROCESS

  • Kim, Joo-Mok;Kim, Yun-Kyong
    • Journal of applied mathematics & informatics
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    • v.33 no.1_2
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    • pp.203-210
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    • 2015
  • We consider fractional Brownian motion and FARIMA process with Gaussian innovations and show that the suitably scaled distributions of the FARIMA processes converge to fractional Brownian motion in the sense of finite dimensional distributions. We figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, d, 0) by using R/S method. Finally, we display power spectrum density of FARIMA process.

ESTIMATION OF HURST PARAMETER AND MINIMUM VARIANCE SPECTRUM

  • Kim, Joo-Mok
    • Korean Journal of Mathematics
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    • v.26 no.2
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    • pp.155-166
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    • 2018
  • Consider FARIMA time series with innovations that have infinite variances. We are interested in the estimation of self-similarities $H_n$ of FARIMA(0, d, 0) by using modified R/S statistic. We can confirm that the $H_n$ converges to Hurst parameter $H=d+\frac{1}{2}$. Finally, we figure out ARMA and minimum variance power spectrum density of FARIMA processes.

The Performance of Time Series Models to Forecast Short-Term Electricity Demand

  • Park, W.G.;Kim, S.
    • Communications for Statistical Applications and Methods
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    • v.19 no.6
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    • pp.869-876
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    • 2012
  • In this paper, we applied seasonal time series models such as ARIMA, FARIMA, AR-GARCH and Holt-Winters in consideration of seasonality to forecast short-term electricity demand data. The results for performance evaluation on the time series models show that seasonal FARIMA and seasonal Holt-Winters models perform adequately under the criterion of Mean Absolute Percentage Error(MAPE).

Performance Analysis of Internet Traffic Forecasting Model (인터넷 트래픽 예측 모형 성능 분석 연구)

  • Kim, S.;Ha, M.H.;Jung, J.Y.
    • The Korean Journal of Applied Statistics
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    • v.24 no.2
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    • pp.307-313
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    • 2011
  • In this paper, we compare performance of three models. The Holt-Winters, FARIMA and ARGARCH models, are used in predicting internet traffic data for analysis of traffic characteristics. We first introduce the time series models and apply them to real traffic data to forecast. Finally, we examine which model is the most suitable for explaining the long memory, the characteristics of the traffic material, and compare the respective prediction performance of the models.

Bivariate long range dependent time series forecasting using deep learning (딥러닝을 이용한 이변량 장기종속시계열 예측)

  • Kim, Jiyoung;Baek, Changryong
    • The Korean Journal of Applied Statistics
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    • v.32 no.1
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    • pp.69-81
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    • 2019
  • We consider bivariate long range dependent (LRD) time series forecasting using a deep learning method. A long short-term memory (LSTM) network well-suited to time series data is applied to forecast bivariate time series; in addition, we compare the forecasting performance with bivariate fractional autoregressive integrated moving average (FARIMA) models. Out-of-sample forecasting errors are compared with various performance measures for functional MRI (fMRI) data and daily realized volatility data. The results show a subtle difference in the predicted values of the FIVARMA model and VARFIMA model. LSTM is computationally demanding due to hyper-parameter selection, but is more stable and the forecasting performance is competitively good to that of parametric long range dependent time series models.

A Study on Internet Traffic Forecasting by Combined Forecasts (결합예측 방법을 이용한 인터넷 트래픽 수요 예측 연구)

  • Kim, Sahm
    • The Korean Journal of Applied Statistics
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    • v.28 no.6
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    • pp.1235-1243
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    • 2015
  • Increased data volume in the ICT area has increased the importance of forecasting accuracy for internet traffic. Forecasting results may have paper plans for traffic management and control. In this paper, we propose combined forecasts based on several time series models such as Seasonal ARIMA and Taylor's adjusted Holt-Winters and Fractional ARIMA(FARIMA). In combined forecasting methods, we use simple-combined method, MSE based method (Armstrong, 2001), Ordinary Least Squares (OLS) method and Equality Restricted Least Squares (ERLS) method. The results show that the Seasonal ARIMA model outperforms in 3 hours ahead forecasts and that combined forecasts outperform in longer periods.

Performance Evaluation of Time Series Models using Short-Term Air Passenger Data

  • Park, W.G.;Kim, S.
    • The Korean Journal of Applied Statistics
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    • v.25 no.6
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    • pp.917-923
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    • 2012
  • We perform a comparison of time series models that include seasonal ARIMA, Fractional ARIMA, and Holt-Winters models; in addition, we also consider hourly and daily air passenger data. The results of the performance evaluation of the models show that the Holt-Winters methods outperforms other models in terms of MAPE.

A study on electricity demand forecasting based on time series clustering in smart grid (스마트 그리드에서의 시계열 군집분석을 통한 전력수요 예측 연구)

  • Sohn, Hueng-Goo;Jung, Sang-Wook;Kim, Sahm
    • The Korean Journal of Applied Statistics
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    • v.29 no.1
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    • pp.193-203
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    • 2016
  • This paper forecasts electricity demand as a critical element of a demand management system in Smart Grid environment. We present a prediction method of using a combination of predictive values by time series clustering. Periodogram-based normalized clustering, predictive analysis clustering and dynamic time warping (DTW) clustering are proposed for time series clustering methods. Double Seasonal Holt-Winters (DSHW), Trigonometric, Box-Cox transform, ARMA errors, Trend and Seasonal components (TBATS), Fractional ARIMA (FARIMA) are used for demand forecasting based on clustering. Results show that the time series clustering method provides a better performances than the method using total amount of electricity demand in terms of the Mean Absolute Percentage Error (MAPE).

Flexible Multimedia Streaming Based on the Adaptive Chunk Algorithm (적응 청크 알고리즘 기반 멀티미디어 스트리밍 알고리즘)

  • Kim Dong-Hwan;Kim Jung-Keun;Chang Tae-Gyu
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.54 no.5
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    • pp.324-326
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    • 2005
  • An adaptive Chunk algorithm is newly devised and a collaborative streaming is designed for high quality multimedia streaming service under time varying traffic conditions. An LMS based prediction filter is used to compensate the effect of time varying background traffic of the WAN. The underflow is generated for the $20\~28\%$ of the data stored in the central server by applying the FARIMA(Fractional Autoregressive Integrated Moving Average) traffic modeling method. The proposed algorithm is tested with the MPEG-2 video files and compensates $71\~85\%$ of central stream underflow.