E jurnal Matematika

Number Vol.3 (4), 2014

130-137
PENERAPAN METODE BOOTSTRAP RESIDUAL DALAM MENGATASI BIAS PADA PENDUGA PARAMETER ANALISIS REGRESI

Authors: Ni Made Metta Astari, Ni Luh Putu Suciptawati, I Komang Gde Sukarsa

Abstract

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Statistical analysis which aims to analyze a linear relationship between the independent variable and the dependent variable is known as regression analysis. To estimate parameters in a regression analysis method commonly used is the Ordinary Least Square (OLS). But the assumption is often violated in the OLS, the assumption of normality due to one outlier. As a result of the presence of outliers is parameter estimators produced by the OLS will be biased. Bootstrap Residual is a bootstrap method that is applied to the residual resampling process. The results showed that the residual bootstrap method is only able to overcome the bias on the number of outliers 5% with 99% confidence intervals. The resulting parameters estimators approach the residual bootstrap values OLS initial allegations were also able to show that the bootstrap is an accurate prediction tool. Keywords: regression analysis, outlier, biases, bootstrap residuals

138-145
PERAMALAN KUNJUNGAN WISATAWAN MENGGUNAKAN MODEL ARMAX DENGAN NILAI KURS DAN EKSPOR-IMPOR SEBAGAI FAKTOR EKSOGEN

Authors: Putu Ika Oktiyari Laksmi, Komang Dharmawan, Luh Putu Ida Harini

Abstract

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Forecasting is science to estimate occurrence of the future. This matter can be conducted by entangling intake of past data and place to the next period with a mathematical form. This research aims to estimate the number of foreign tourists visiting Bali models using autoregressive moving average exogenous (ARMAX). The data used in this study is the number of tourists in Australia and the number of tourists in the RRC as a variable Y, and foreign currency exchange rate AUD, Chinese Yuan, and Export Import as the X factor from the period July 2009 to July 2014. In the analysis can be obtained in the best ARMAX models of the number of tourists in Australia is ARMAX(1,2,2) and the best model of the number of tourists in the RRC does not exist because the data for the ARMAX model parameters tourists no significant RRC. Keywords: forecasting, ARMAX model, and the number tourists.

146-153
KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS

Authors: Hany Devita, I Komang Gde Sukarsa, I Putu Eka N. Kencana

Abstract

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Number of views: 519

Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity. Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model. Keywords: ordinary least square,multicollinearity, Generalized Ridge Regression,Jackknife Ridge Regression

154-159
PENENTUAN HARGA KONTRAK OPSI TIPE EROPA MENGGUNAKAN METODE QUASI MONTE CARLO DENGAN BARISAN KUASI-ACAK HALTON

Authors: I Gusti Putu Ngurah Mahayoga, Komang Dharmawan, Luh Putu Ida Harini

Abstract

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Number of views: 492

Penelitian ini bertujuan untuk mengetahui keakuratan hasil simulasi harga saham untuk menentukan harga opsi call dari metode Monte Carlo dan metode Quasi Monte Carlo dengan menggunakan program Matlab. Harga standar yang digunakan untuk membandingkan kedua metode tersebut akan dihitung dengan metode Black-Scholes. Nilai error yang dihitung menggunakan metode MAPE (Mean Absolute Percentage Error) digunakan sebagai acuan dalam perbandingan. Selain keakuratan simulasi harga saham, kecepatan eksekusi program Matlab kedua metode juga dihitung untuk efisiensi waktu. Tahap pertama, menentukan variabel-variabel yang digunakan untuk menghitung lintasan harga saham pada waktu ke-t pada saat mensimulasikan harga saham. Tahap kedua, menghitung harga standar menggunakan metode Black-Scholes. Tahap ketiga, mensimulasikan harga saham dengan metode Monte Carlo dan Quasi Monte Carlo. Setelah mensimulasikan harga saham, catat waktu eksekusi program Matlab, lalu dihitung nilai pay-off dari opsi call, kemudian menaksir harga opsi call dengan merata-ratakan seluruh nilai pay-off dari masing-masing iterasi. Tahap terakhir, menghitung error dari kedua metode simulasi dengan metode MAPE lalu membandingkannya. Hasil penelitian ini menunjukkan bahwa metode Quasi Monte Carlo lebih akurat karena menghasilkan nilai error yang lebih kecil, artinya hasil simulasinya mendekati harga standar. Sedangkan untuk waktu eksekusi program, metode Monte Carlo lebih baik di semua iterasi. Keywords: MAPE, Monte Carlo, Opsi, Quasi-random Halton, Quasi Monte Carlo.

160-167
APLIKASI ALGORITMA GENETIKA UNTUK MERAMALKAN KONSUMSI PREMIUM KOTA DENPASAR

Authors: Victor Mallang, Ketut Jayanegara, Made Asih3, I Putu Eka N. Kencana

Abstract

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Number of views: 506

This research aimed to forecast the gasoline demand at Denpasar using genetic algorithm method. This algorithm was selected because of easy to implement and its ability to find acceptable solution quickly. This algorithm works by searching the best individu according to fitness function defined. The series data used in the research were 60 observations of monthly gasoline demand at Denpasar for period January 2009 through December 2013. By observing the Partial Autocorrelation Function (PACF) plot, we found the last lag before the series become stationer was sixth lag. Based on this finding, we decided the best individu was represented by six genes. This individu, in addition, was used to make in-sample forecasting. The forecasted data had mean absolute error (MAE) as much as 553,27 kiloliters. For one semester out-of sample forecast, we found gasoline consumption fluctuated with lowest and highest consumption were for February 2014 and June 2014, respectively. Keywords: forecasting, gasoline demand, genetic algorithm, MAE