Estimasi Densitas Mulus dengan Metode Wavelet (Wavelet Method in Smooth Density Estimation)

Let i = 1,2,…,n be independent observation data from a distribution with an unknown density function f . The function f could be estimated by parametric and nonparametric approach. In nonparametric approach, the function f is assumed to be a smooth function or quadratic integrable function, so the function f could be estimated by kernel estimator or orthogonal series estimator, especially by Fourier series estimator. Another orthogonal series estimator which could be use to estimate f is wavelet estimator. Wavelet estimator is an extention of Fourier series estimator but it has caracteristics like the kernel estimator. Key words : smooth density, kernel estimator, Fourier series estimator, wavelet estimator

The Adequateness of Wavelet Based Model for Time Series

In general, time series is modeled as summation of known information i.e. historical information components, and unknown information i.e. random component. In wavelet based model, time series is represented as linear model of wavelet coecients. Wavelet based model captures the time series feature perfectly when the historical information components dominate the process. In other hand, it has low enforcement when the random component dominates the process. This paper proposes an eort to develop the adequateness of wavelet based model, when the random component dominated the process. By weighted summation, the data is carried to the new form which has higher dependencies. Consequently, wavelet based model will work better. Finally, it is hoped that the better prediction of wavelet based model will be carried to the original prediction in reverting process

H-WEMA: A New Approach of Double Exponential Smoothing Method

A popular smoothing technique commonly used in time series analysis is double exponential smoothing. Basically, it’s an improvement of simple exponential smoothing which does the exponential filter process twice. Many researchers had developed the technique, hence Brown’s double exponential smoothing and Holt’s double exponential smoothing. Here, we introduce a new approach of double exponential smoothing, called H-WEMA, which combines the calculation of weighting factor in weighted moving average with Holt’s double exponential smoothing method. The proposed method will then be tested on Jakarta Stock Exchange (JKSE) composite index data. The accuracy and robustness level of the proposed method will then be examined by using mean square error and mean absolute percentage error criteria, and be compared to other conventional methods

Brown’s Weighted Exponential Moving Average Implementation in Forex Forecasting

In 2016, a time series forecasting technique which combined the weighting factor calculation formula found in weighted moving average with Brown’s double exponential smoothing procedures had been introduced. The technique is known as Brown’s weighted exponential moving average (B-WEMA), as a new variant of double exponential smoothing method which does the exponential filter processes twice. In this research, we will try to implement the new method to forecast some foreign exchange, or known as forex data, including EUR/USD, AUD/USD, GBP/USD, USD/JPY, and EUR/JPY data. The time series data forecasting results using B-WEMA then be compared with other conventional and hybrid moving average methods, such as weighted moving average (WMA), exponential moving average (EMA), and Brown’s double exponential smoothing (B-DES). The comparison results show that B-WEMA has a better accuracy level than other forecasting methods used in this research

Transformasi Wavelet Diskret Untuk Data Time Series

Untuk mengolah atau menganalisis data yang mempunyai dimensi tinggi sangat sulit bahkan dengan sistem komputer modern sekalipun. Suatu pendekatan yang digunakan adalah mengurangi dimensi data yang disebut dengan reduksi dimensi. Transformasi wavelet diskret (TWD) merupakan salah satu teknik reduksi dimensi, yaitu teknik dekomposisi multi resolusi untuk mengatasi masalah pemodelan yang menghasilkan sinyal representasi lokal yang baik pada domain waktu dan domain frekuensi. Jenis wavelet yang digunakan adalah wavelet Haar. Pada penelitian ini, peneliti akan membahas penanganan data time series berdimensi tinggi menggunakan TWD dan mengaplikasikannya dalam data time series. Kata Kunci : reduksi dimensi, wavelet Haar, transformasi wavelet diskret

Pemilihan Model Regresi Linier Dengan Bootstrap

Tulisan ini membicarakan tentang penerapan bootstrap untuk pemilihan model regresi linier terbaik. Model regresi linier terbaik yang terpilih adalah model dengan estimasi sesatan prediksi kuadrat minimal atas semua model regresi yang mungkin yaitu sebanyak 2p-1 model dengan p: banyaknya variabel prediktor. Metode Bootstrap memilih suatu model dengan meminimalkan rata-rata sesatan prediksi kuadrat berdasarkan resampling data yang dibangkitkan melalui pasangan data dan residual, dengan mempertimbangkan juga variabel prediktor yang terlibat sesedikit mungkin. Pemilihan variabel berdasarkan bootstrap pasangan data dan bootstrap residual dengan n ukuran sampel bootstrap adalah konsisten. Dan jika ukuran sampel bootstrap diambil m dengan , pemilihan variabel bootstrap juga konsisten. Hasil dari suatu simulasi dengan SPLUS disajikan dalam tulisan ini

Simulation of queue with cyclic service in signalized intersection system

The simulation was implemented by modeling the queue with cyclic service in the signalized intersection system. The service policies used in this study were exhaustive and gated, the model was the M/M/1 queue, the arrival rate used was Poisson distribution and the services rate used was Exponential distribution. In the gated service policy, the server served only vehicles that came before the green signal appears at an intersection. Considered that there were 2 types of exhaustive policy in the signalized intersection system, namely normal exhaustive (vehicles only served during the green signal was still active), and exhaustive (there was the green signal duration addition at the intersection, when the green signal duration at an intersection finished). The results of this queueing simulation program were to obtain characteristics and performance of the system, i.e. average number of vehicles and waiting time of vehicles in the intersection and in the system, as well as system utilities. Then from these values, it would be known which of the cyclic service policies (normal exhaustive, exhaustive and gated) was the most suitable when applied to a signalized intersection syste

Penerapan Algoritma Genetika Untuk Optimasi Penjadwalan Tebangan Hutan

Scheduling Cuts Away Forest is one of problem met at forestry area. All important problem in finalizing this problem is to determine forest check which will be cut away with a purpose to maximizes yield wood volume in each period cuts away and remain to maintains everlasting forest concept. Method which has been developed to finalize this problem is apply linear program with simplex method. At this method every step is taken based on exact formula is assessed unsatisfying good to finalize this problem. Genetics algorithm is one of alternative of solution of scheduling problems cuts away this forest. This idea of this algorithm comes from the Evolution Theory of Charles Darwin, which is only the best route was choosen. An individual was being choosen from a parent population and then recombined to another individual that has been choosen from another parent population to create a new individu. This new individual expected to be better from the rest individu at the population. With this method, the genetic algorithm found to be able to offer a best Scheduling Cuts Away Forest Problem