• Korean Journal of Mathematics
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• v.17 no.4
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• pp.399-409
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• 2009

We study the weak convergence of various models to Fractional Brownian motion. First, we consider arima process and ON/OFF source model which allows for long packet trains and long inter-train distances. Finally, we figure out power spectrum density as a Fourier transform of autocorrelation function of arima model and binary signal model.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.1053-1061
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• 2013

In this paper, we propose the time series forecasting models for internet traffic with long memory and heteroscedasticity. To control and forecast traffic volume, we first introduce the traffic forecasting models which are determined by the volatility and heteroscedasticity of the traffic. We then analyze and predict the heteroscedasticity and the long memory properties for forecasting traffic volume. Depending on the characteristics of the traffic, Fractional ARIMA model, Fractional ARIMA-GARCH model are applied and compared with the MAPE(Mean Absolute Percentage Error) Criterion.

• 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.

• 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.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.8B
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• pp.667-680
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• 2008

In this work, we present the results of our empirical study on 802.11 wireless LAN network traffic. We collect the packet trace from existing campus wireless LAN infra-structure. We analyzed four different data sets: aggregate traffic, upstream traffic, downstream traffic, tcp only packet trace from aggregate traffic. We analyze the time series aspect of underlying traffic (byte count process and packet count process), marginal distribution of time series, and packet size distribution. We found that in all four data sets there exist long-range dependent property in byte count and packet count process. Inter-arrival distribution is well fitted with Pareto distribution. Upstream traffic, i.e. from the user to Internet, exhibits significant difference in its packet size distribution from the rests. Average packet size of upstream traffic is 151.7 byte while average packet size of the rest of the data sets are all greater than 260 bytes. Packets with full data payloads constitutes 3% and 10% in upstream traffic and the downstream traffic, respectively. Despite the significant difference in packet size distribution, all four data sets have similar Hurst values. The Hurst alone does not properly explain the stochastic characteristics of the underlying traffic. We model the underlying traffic using fractional-ARIMA (FARIMA) and fractional Gaussian Noise (FGN). While the fractional Gaussian Noise based method is computationally more efficient, FARIMA exhibits superior performance in accurately modeling the underlying traffic.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.415-422
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• 2012

In this paper, we first the compare the performance of Holt-Winters, FSARIMA, AR-GARCH and Seasonal AR-GARCH models with in the short term based data. The results of the compared data show that the Holt-Winters model outperformed other models in terms of forecasting accuracy.

• 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).

• 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.