Double Exponential Research Articles

Short-term Forecasting of Air Passengers based on Hybrid Rough Set and Double Exponential Smoothing Models

Short-term Forecasting of Air Passengers based on Hybrid Rough Set and Double Exponential Smoothing Models

Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using Sinc Nyström method

ABSTRACTIn this paper, a double-exponential (DE) Sinc Nyström method is utilized to solve nonlinear two-dimensional Fredholm integral equations of the second kind. Using the DE transformation, the Sinc quadrature rule for a definite integral is extended to double integral over a rectangular region. Therefore, a nonlinear Fredholm integral equation is reduced to a system of nonlinear algebraic equations, which is solved using the Newton iteration method. Convergence analysis shows that the proposed method can converge exponentially. Several numerical examples are provided to demonstrate the high efficiency and accuracy of the proposed method.

Bimodal Soil Pore Structure Investigated by a Combined Soil Water Retention Curve and X‐Ray Computed Tomography Approach

Core Ideas Soil water retention curves of the paddy soil were bested fitted with bimodal models. Computed‐tomography imaging and retention curves generated similar bimodal pore structure. Combined use of organic and inorganic fertilizers increased structural porosity. Textural porosity was not affected by fertilization treatments. Well‐structured soils are considered to have bimodal pore structure, including textural pores between particles and structural pores between aggregates. Pore structure can be inferred from the soil water retention curve (SWRC) but our understanding of the 3‐D pore geometry that regulates this curve is limited. This study investigated the pore structure of a paddy soil under different fertilization regimes by both SWRC and X‐ray micro‐computed tomography (micro‐CT) imaging with the aim of comparing the two methods. Undisturbed soil aggregates and cores were collected from the surface layer of long‐term unfertilized (CK), inorganically fertilized (NPK), and organically and inorganically fertilized (NPKOM) paddy soils. Aggregates and cores were scanned with micro‐CT and pore structures were analyzed. The SWRCs were measured on the same CT‐scanned cores. Three unimodal models, three bimodal models, and one trimodal model were evaluated for fitting the SWRC and to derive soil pore size distribution (PSD). Results showed the SWRC of the paddy soil were best fitted with the bimodal lognormal (BLN) and double‐exponential (DE) models, with the derived PSD showing distinct bimodality. The micro‐CT images revealed the hierarchy structure of the paddy soil and a bimodal pattern in the PSDs. The structural porosities from BLN, DE models and CT imaging were consistent and correlated with the natural logarithm of saturated hydraulic conductivity. Long‐term application of NPKOM increased structural porosity though no significant differences were recorded in the textural porosity compared with the NPK and CK treatment, while the latter two showed a near identical pore structure. These results demonstrated the benefits of both approaches especially for soil structures with a bimodal pore structure such as the well‐structured paddy soil.

Perbandingan Metode Holt Eksponential Smoothing dan Winter Eksponential Smoothing Untuk Peramalan Penjualan Souvenir

UD. Fajar Jaya is a trading business unit engaged in the supply of souvenirs. But in the management of the business there are some problems of which are UD. Fajar Jaya can not predict how the optimal number of souvenirs that must be provided to customers on every item souvenirs are sold. This causes the service to consumers less than the maximum, especially at certain moments sales of souvenirs (example: glass souvenirs) jumped dramatically from the number of average sales. To overcome the above, the authors propose to forecast the level of sales of souvenirs using Holt and Winter methods that exist in the development of Exponential Smoothing (ES) method. From the application of the two methods, then will make comparison of effectiveness of method which measured through actual data accuracy and forecasting result by knowing forecast error level. From the research results obtained forecasting results for Holt Double Exponential Smoothing method in July of 2017 is amounted to 599 items that may be sold with MAD forecasting error rate of 10.54 and MAPE of 3.70%. As for forecasting using Winter Exponential Smoothing method in July of 2017 is 549.6 items that may be sold with MAD 0.02 and MAPE error rate of 2.55%. The conclusion that can be drawn from the research that has been done on sales data souvenirs on UD. Fajar Jaya is that the Winter Exponential Smoothing method is more suitable to be applied in case study of souvenir sales in UD. Fajar Jaya is more than Holt Double Exponential Smoothing method.

Advanced Control for Energy Management of Grid-Connected Hybrid Power Systems in the Sugar Cane Industry

This work presents a process supervision and advanced control structure, based on Model Predictive Control (MPC) coupled with disturbance estimation techniques and a finite-state machine decision system, responsible for setting energy productions set-points. This control scheme is applied to energy generation optimization in a sugar cane power plant, with non-dispatchable renewable sources, such as photovoltaic and wind power generation, as well as dispatchable sources, as biomass. The energy plant is bound to produce steam in different pressures, cold water and, imperiously, has to produce and maintain an amount of electric power throughout each month, defined by contract rules with a local distribution network operator (DNO). The proposed predictive control structure uses feedforward compensation of estimated future disturbances, obtained by the Double Exponential Smoothing (DES) method. The control algorithm has the task of performing the management of which energy system to use, maximize the use of the renewable energy sources, manage the use of energy storage units and optimize energy generation due to contract rules, while aiming to maximize economic profits. Through simulation, the proposed system is compared to a MPC structure, with standard techniques, and shows improved behavior.

Data completion with Hilbert transform over plane rectangle: Technique renovation for the Grad‐Shafranov reconstruction

AbstractHilbert transforms (HT) have first been used to build the essential technique of Grad‐Shafranov (GS) reconstruction by Li et al. (2013), where the problem of ill posedness in GS reconstruction has been thoroughly investigated. In this study, we present an extended Hilbert transform (EHT) over the plane rectangle. In contrast to previous one (HT over the unit circular region), corner singularities are introduced into these new formulae. It is confronted by problems like the integral with both endpoint singularities, and the semiinfinite integral with one endpoint singularity, as these EHT formulae are used to rebuild the essential technique of GS reconstruction. Two additional mathematic tools are adopted in this study. First, high‐accuracy quadrature schemes are constructed for those improper integrals based on the double exponential (DE) transformations. Benchmark testing with the analytic solutions on a rectangular boundary has shown the efficiency and robustness of the EHT formulae. Second, the data completion or the inverse boundary value problem is solved with the help of a truncated Chebyshev series, which approximates the unknown boundary gradients in very high efficiency under the only assumption that they are Lipschitz continuous on each side of the rectangle. Combining the introduced EHT formulae and the two needed mathematic tools, the essential technique of GS reconstruction is formulated into a linear system of Fredholm equations of the first kind. Then a three‐parameter Tikhonov regularization scheme is developed to deal with the ill‐posed linear operators appearing in the discretized linear system. This new approach for data completion over the plane rectangle is benchmarked with the analytic solutions. Numerical experiments highlight the efficiency and robustness of the proposed method.

Numerical solution of system of Volterra integral equations with weakly singular kernels and its convergence analysis

In this paper, efficient and computationally attractive methods based on the Sinc approximation with the single exponential (SE) and double exponential (DE) transformations for the numerical solution of a system of Volterra integral equations with weakly singular kernels are presented. Simplicity for performing even in the presence of singularities is one of the advantages of Sinc methods. Convergence analysis of the proposed methods is given and an exponential convergence is achieved as well. Numerical results are presented which demonstrate the efficiency and high accuracy of the proposed methods.

Application of Several Models for the Forecasting of the Container Throughput of the Abidjan Port in Ivory Coast

The Abidjan Port in Ivory Coast has the second highest volume of Container Throughput in West Africa and aims to become a hub Port for the region and one of the most developed Port in Africa in the coming years. In this article, several Forecasting Models are applied to accurately forecast the Abidjan Port Container Throughput. These models are the Grey model, the Linear Regression model, the Double Exponential Smoothing model and a Combination Forecast model. After the application of each model, their results have been compared with the mean absolute percentage error. From their results, the Double Exponential Smoothing model has got the smallest error and been found to have the best data available on the research work, becoming at the same time, the best forecasting model for the Abidjan Port Container Throughput. A forecast of the Abidjan Port Container Throughput was finally made for the period covering the year 2015 up to the year 2020.

Forecasting and evaluation for raisin export in turkey

Turkey is the world's second largest raisin producer after the United States and the leading exporter, accounting to 25% of the world's total raisin production and 40–45% of total raisin exports. The European Union is the top export destination for Turkish raisins receiving an average of 80 percent of all Turkish raisin exports. The main objective of the study is to forecast Turkey's raisin export. A time series modeling approach (Double Exponential Smoothing) has been used to forecast raisin export in Turkey. The forecasts for the export of raisin in Turkey have been made for the next five years using by annual data on 1982–2015 years in this study. The forecast results have shown that the raisin export in Turkey will be around 209,738 tons in 2016.

Rainfall prediction and meteorological drought analysis in the Sakae Krang River basin of Thailand

Rainfall was predicted and used to analyze the severity levels of meteorological drought in the Sakae Krang River basin. Three forecasting models based on the Time Series Prediction technique, Single Moving Average, Simple Exponential Smoothing and Double Exponential Smoothing (Holt's model) were used to predict rainfall using the data collected from five rain gauge stations between 1970 and 2014. The minimum mean percentage error (MPE) score was used to indicate the accuracy of prediction. A standardized precipitation index (SPI) was used to indicate the drought severity levels in the Sakae Krang River basin between 1970 and 2015. The Simple Exponential Smoothing model produced the most accurate rainfall prediction followed by Double Exponential Smoothing (Holt's model) and the Single Moving Average model with MPE scores of 28%, 31% and 36%, respectively. The drought analysis results indicated that from 1970 to 2014, there was no clear trend in meteorological drought in the Sakae Krang River basin. In 2015, the meteorological drought severity level analysis of the sub-basins of the Sakae Krang River basin was graded as moderate drought for the lower part of Mae Nam Sakae Krang 1 and mild drought for Nam Mae Wong, the lower part of Mae Nam Sakae Krang 2, Khlong Pho and Huai Thap Salao with SPI scores of −1.01, −0.97, −0.91, −0.57 and −0.32, respectively.

A New Approach of Brown’s Double Exponential Smoothing Method in Time Series Analysis

Double Exponential Smoothing is an improvement of Simple Exponential Smoothing, also known as Exponential Moving Average, which does the exponential filter process twice. It’s usually been used to predict the future data in time series analysis, where there is a trend in the data. In this paper, we aim to introduce a new approach of Brown’s Double Exponential Smoothing in time series analysis. The new approach will combine the calculation of weighting factor in Weighted Moving Average and implement the results with Brown’s Double Exponential Smoothing method. The proposed method will be tested on Jakarta Stock Exchange (JKSE) composite index data. The result of the proposed method shows a promising result in this work.

Estimation of Nuclear Counting by a Nonlinear Filter Based on a Hypothesis Test and a Double Exponential Smoothing

Online nuclear counting represents a challenge due to the stochastic nature of radioactivity. The counting data have to be filtered in order to provide a precise and accurate estimation of the count rate, while ensuring a response time compatible with the application in view. An innovative filter is presented in this paper to address this issue. The filter is nonlinear and based on a Centered Significance Test (CST) providing a local maximum likelihood estimation of the signal. This nonlinear approach allows enables to smooth the counting signal while maintaining a fast response when brutal change in activity occurs. The filter is then improved by the implementation of a Brown’s double Exponential Smoothing (BES). The filter has been validated and compared to other state-of-the-art smoothing filters. The CST* filter shows a significant improvement compared to all tested smoothing filters.

Forecasting the REITs and stock indices: Group Method of Data Handling Neural Network approach

If there is long-term memory in property stocks and REITs prices, historical data is relevant for future prices prediction. Despite previous research adopted various different methods to forecast future asset prices by using historical data; we attempted to forecast the REITs and stock indices by Group Method of Data Handling (GMDH) neural network method with Hurst which is the first of its kind. Our results showed that GMDH neural network performed better than the classical forecasting algorithms such as Single Exponential Smooth, Double Exponential Smooth, ARIMA and back-propagation neural network. The research results also provide useful information for investors when they make investment decisions.

On the very accurate numerical evaluation of the Generalized Fermi–Dirac Integrals

We indicate a new and a very accurate algorithm for the evaluation of the Generalized Fermi–Dirac Integral with a relative error less than 10−20. The method involves Double Exponential, Trapezoidal and Gauss–Legendre quadratures. For the residue correction of the Gauss–Legendre scheme, a simple and precise continued fraction algorithm is used.

Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces

We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider the Hardy space of functions that are analytic in a strip region around the real axis, being characterized by a weight function $w$ that determines the decay rate of its elements in the neighborhood of infinity. Such a space is considered as a set of functions that are transformed by variable transformations that realize a certain decay rate at infinity. Popular examples of such transformations are given by the single exponential (SE) and double exponential (DE) transformations for the SE-Sinc and DE-Sinc formulas, which are very accurate owing to the accuracy of sinc interpolation in the weighted Hardy spaces with single and double exponential weights $w$, respectively. However, it is not guaranteed that the sinc formulas are optimal in weighted Hardy spaces, although Sugihara has demonstrated that they are near optimal. An explicit form for an optimal approximation formula has only been given in weighted Hardy spaces with SE weights of a certain type. In general cases, explicit forms for optimal formulas have not been provided so far. We adopt a potential theoretic approach to obtain almost optimal formulas in weighted Hardy spaces in the case of general weight functions $w$. We formulate the problem of designing an optimal formula in each space as an optimization problem written in terms of a Green potential with an external field. By solving the optimization problem numerically, we obtain an almost optimal formula in each space. Furthermore, some numerical results demonstrate the validity of this method. In particular, for the case of a DE weight, the formula designed by our method outperforms the DE-Sinc formula.

Comparison between ARIMA and DES Methods of Forecasting Population for Housing Demand in Johor

Forecasting accuracy is a primary criterion in selecting appropriate method of prediction. Even though there are various methods of forecasting however not all of these methods are able to predict with good accuracy. This paper presents an evaluation of two methods of population forecasting for housing demand. These methods are Autoregressive Integrated Moving Average (ARIMA) and Double Exponential Smoothing (DES). Both of the methods are principally adopting univariate time series analysis which uses past and present data for forecasting. Secondary data obtained from Department of Statistics, Malaysia was used to forecast population for housing demand in Johor. Forecasting processes had generated 14 models to each of the methods and these models where evaluated using Mean Absolute Percentage Error (MAPE). It was found that 14 of Double Exponential Smoothing models and also 14 of ARIMA models had resulted to 1.674% and 5.524% of average MAPE values respectively. Hence, the Double Exponential Smoothing method outperformed the ARIMA method by reducing 4.00 % in forecasting model population for Johor state. These findings help researchers and government agency in selecting appropriate forecasting model for housing demand.

An Approach for Energy Efficient Dynamic Virtual Machine Consolidation in Cloud Environment

Nowadays, as the use of cloud computing service becomes more extensive and the customers welcome this service, an increasing trend in energy consumption and operational costs of these centers may be seen. To reduce operational costs, the providers should decrease energy consumption to an extent that Service Level Agreement (SLA) maintains at a desirable level. This paper adopts the virtual machine consolidation problem in cloud computing data centers as a solution to achieve this goal, putting forward solutions to make the decision regarding the necessity of migration from hosts and finding appropriate hosts as destinations of migration. Using time-series forecasting method and Double Exponential Smoothing (DES) technique, the proposed algorithm predicts CPU utilization in near future. It also proposes an optimal equation for the dynamic lower threshold. Comparing current and predicted CPU utilization with dynamic upper and lower thresholds, this algorithm identifies and categorizes underloaded and overloaded hosts. According to this categorization, migration then occurs from the hosts that meet the necessary conditions for migration. This paper identifies a certain type of hosts as “troublemaker hosts”. Most probably, the process of prediction and decision making regarding the necessity of migration will be disrupted in the case of these hosts. Upon encountering this type of hosts, the algorithm adopts policies to modify them or switch them to sleep mode, thereby preventing the adverse effects caused by their existence. The researchers excluded all overloaded, prone-to-be-overloaded, underloaded, and prone-to-be-underloaded hosts from the list of suitable hosts to find suitable hosts as destinations of migration. An average improvement of 86.2%, 28.4%, and 87.2% respectively for the number of migrations of virtual machines, energy consumption, and SLA violation is among the simulation achievements of this algorithm using Clouds tool.

The Double Exponential Formula as a Gauss Quadratures Replacement for Numerical Integration

The Double Exponential Formula as a Gauss Quadratures Replacement for Numerical Integration

Stochastic Volatility Double Jump-Diffusions Model: The Importance of Distribution Type of Jump Amplitude

This research examines if there exists an appealing distribution for jump amplitude in the sense that with this distribution, the stochastic volatility double jump-diffusions (SVJJ) model would potentially have a superior option market fit while keeping a sound balance between reality and tractability. We provide a general methodology for pricing vanilla options via Fourier cosine series expansion method, in the setting of Heston's SVJJ (HSVJJ) model that may allow a range of jump amplitude distributions. Example applications include the normal (N) distribution, the exponential (E) distribution and the asymmetric double exponential (Db-E) distribution, regarding to analytical tractability for options and economical interpretation. An illustrative example examines the implications of HSVJJ model in capturing option 'smirks'. This example highlights the impacts on implied volatility surface of various jump amplitude distributions, through both extensive model calibrations and carefully designed implied-volatility impacting experiments. Numerical results show that, with the Db-E jump distribution, the HSVJJ model not only captures the implied volatility smile and smirk, but also the 'sadness'.

MODEL EKSPONENSIAL GANDA PADA PROSES STOKASTIK (STUDI KASUS DI STASIUN PURWOSARI)

In general, mathematical modeling is divided into two, namely the model of deterministic and stochastic models. On stochastic modeling involves several processes among them are the Poisson process, the process of Bernoulli, Gaussian processes, the process of renewal and other processes. Specifically for the Poisson process often found in modeling queuing theory. At Poisson process there are four kinds of sub model that can be formed that is Double Poisson models, Exponential Poisson models, Poisson Exponential model, and Double Exponential models. In this paper will discuss the Double Exponential model in stochastic processes , specifically for the Poisson process. Analysis was performed on the data arrival time and service time. The model is a model (M / M / c) : ( GD / ~, ~) which is a double exponential model in stochastic processes. Keywords: Double Exponential, Poisson Process, Stochastic Process