E jurnal Matematika

8-13

Authors: Ni Wayan Yuni Cahyani, I Gusti Ayu Made Srinadi, Made Susilawati

Ordinary least square (OLS) is a method that can be used to estimate the parameter in linear regression analysis. There are some assumption which should be satisfied on OLS, one of this assumption is homoscedasticity, that is the variance of error is constant. If variance of the error is unequal that so-called heteroscedasticity. The presence heteroscedasticity can cause estimation with OLS becomes inefficient. Therefore, heteroscedasticity shall be overcome. There are some method that can used to overcome heteroscedasticity, two among those are Box-Cox power transformation and median quantile regression. This research compared Box-Cox power transformation and median quantile regression to overcome heteroscedasticity. Applied Box-Cox power transformation on OLS result

20-25

Authors: Putu Ayu Maziyya, I Komang Gde Sukarsa, Ni Made Asih

In the regression analysis we need a method to estimate parameters to fulfill the BLUE characteristic. There are assumptions that must be fulfilled homoscedasticity one of which is a condition in which the assumption of error variance is constant (same), infraction from the assumptions homoskedasticity called heteroscedasticity. The Consequence of going heteroscedasticity can impact OLS estimators still fulfill the requirements of not biased, but the variant obtained becomes inefficient. So we need a method to solve these problems either by Weighted Least Square (WLS). The purpose of this study is to find out how to overcome heteroscedasticity in regression with WLS. Step of this research was do with the OLS analysis, then testing to see whether there heteroscedasticity problem with BPG method, the next step is to repair the beginning model by way of weighting the data an exact multiplier factor, then re-using the OLS procedure to the data that have been weighted, the last stage is back with a heteroscedasticity test BPG method, so we obtained the model fulfill the assumptions of homoskedasicity. Estimates indicate that the WLS method can resolve the heteroscedasticity, with exact weighting factors based on the distribution pattern of data seen. Keywords: heteroscedasticity, OLS, WLS

138-145

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

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.

154-159

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

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.

92-99

Authors: Juen Ling, I Putu Eka N. Kencana, Tjokorda Bagus Oka

Sentiment analysis is the computational study of opinions, sentiments, and emotions expressed in texts. The basic task of sentiment analysis is to classify the polarity of the existing texts in documents, sentences, or opinions. Polarity has meaning if there is text in the document, sentence, or the opinion has a positive or negative aspect. In this study, classification of the polarity in sentiment analysis using machine learning techniques, that is Naïve Bayes classifier. Criteria for text classification decisions, learned automatically from learning the data. The need for manual classification is still required because training the data derived from manually labeling, the label (feature) refers to the process of adding a description of each data according to its category. In the process of labeling, feature selection is used and performed by chi-square feature selection, to reduce the disturbance (noise) in the classification. The results showed that the frequency of occurrences of the expected features in the true category and in the false category have an important role in the chi-square feature selection. Then classification by Naïve Bayes classifier obtained an accuracy of 83% and a harmonic average of 90.713%. Keywords: chi square, classification, feature selection, machine learning technique, Naïve Bayes, sentiment analysis.

107-115

Authors: Ni Made Rara Keswari, I Wayan Sumarjaya, Ni Luh Putu Suciptawati

Poisson regression is a nonlinear regression that is often used to model count response variable and categorical, interval, or count regressor. This regression assumes equidispersion, i.e., the variance equals the mean. However, in practice, this assumption is often violated. One of this violation is overdispersion in which the variance is greater than the mean. There are several methods to overcome overdispersion. Two of these methods are negative binomial regression and generalized Poisson regression. In this research, binomial negative regression and generalized Poisson regression statistically equally good in handling overdispersion. Keyword: Poisson Regression, Overdispersion, Negative Binomial Regression, Generalized Poisson Regression.

123-129

Authors: I Putu Oka Paramartha, Komang Dharmawan, Desak Putu Eka Nilakusmawati

The aim to determine of the simulation results and to calculate the stock price of Asian Option with Normal Inverse Gaussian (NIG) method and Monte Carlo method using MATLAB program. Results of both models are compared and selected a fair price. Besides to determine simulation accuracy of the stock price, speed of program execution MATLAB is calculated for both models for time efficiency. The first part, set variabels used to calculate the trajectory of stock prices at time t to simulate the stock price at the time. The second part, simulate the stock price with NIG model. The third part, simulate the stock price with Monte Carlo model. After simulating the stock price, calculated the value of the pay-off of the Asian Option, and then estimate the price of Asian Option by averaging the entire value of pay-off from each iteration. The last part, compare result of both models. The results of this research is price of Asian Option calculated using Monte Carlo simulation and NIG. The rates were calculated using the NIG produce a fair price, because of the pricing contract NIG using four parameters α, β, δ, and μ, while Monte Carlo is using only two parameters σ and μ. For execution time of the program, the Monte Carlo model is better in all iterations. Keywords: Option, Asian Option, Normal Inverse Gaussian, NIG, Monte Carlo.

45-52

Authors: NI PUTU NIA IRFAGUTAMI, I GUSTI AYU MADE SRINADI, I WAYAN SUMARJAYA

The presence of outliers in observation can result in biased in parameter estimation using ordinary least square (OLS). Robust regression MM-estimator is one of the estimations methods that able to obtain a robust estimator against outliers. Random sample consensus (ransac) is another method that can be used to construct a model for observations data and also estimating a robust estimator against outliers. Based on the study, ransac obtained model with less biased estimator than robust regression MM-estimator. Keywords: Outlier, Robust Regression, MM-estimate, ransac

64-74

Authors: I GUSTI AYU KOMANG KUSUMA WARDHANI, I NYOMAN WIDANA, NI KETUT TARI TASTRAWATI

The company which provides the pension program needs the actuarial valuation to estimate the fund amount required by the company to pay for pension funding. Actuarial method that used in this research are projected unit credit and invidual level premium method. Through this research be obtained the result of valuation pension benefits with career average salary assumption is lower than the other salary assumptions. On the other hand, the result of normal cost final value valuation using individual level premium method is smaller than projected unit credit method that suits for the participants of the pension funding program. Keywords: Pension Funding, Normal Cost, Projected Unit Credit, Individual Level Premium.

8-16

Authors: DWI LARAS RIYANTINI, MADE SUSILAWATI, KARTIKA SARI

Multicollinearity is a problem that often occurs in multiple linear regression. The existence of multicollinearity in the independent variables resulted in a regression model obtained is far from accurate. Latent root regression is an alternative in dealing with the presence of multicollinearity in multiple linear regression. In the latent root regression, multicollinearity was overcome by reducing the original variables into new variables through principal component analysis techniques. In this regression the estimation of parameters is modified least squares method. In this study, the data used are eleven groups of simulated data with varying number of independent variables. Based on the VIF value and the value of correlation, latent root regression is capable of handling multicollinearity completely. On the other hand, a regression model that was obtained by latent root regression has R_adj^2 value of 0.99, which indicates that the independent variables can explain the diversity of the response variables accurately. Keywords: Multiple Linear Regression, Multicollinearity, Latent Root Regression, Least Squares Method Modified

25-32

Authors: JOKO HADI APRIANTO, G. K. GANDHIADI, DESAK PUTU EKA NILAKUSMAWATI

The rise of credit card users, make banks compete to provide a wide range of offers to attract customers. This study aims to determine the priority criteria selected customers for establishment credit cards by using a fuzzy AHP method. Method fuzzy AHP is a combination of the AHP method and fuzzy method. Fuzzy AHP approach particularly triangular fuzzy number approach to the AHP scale should be able to minimize uncertainty for the results obtained are more accurate. The criteria used for this study is the interest rate , the promo/discount, limit, and annual dues. Based on the steps of calculation of data obtained fuzzy AHP respondents have value CR = 0.049, which means consistent because it meets the standards set CR < 0.10 and that became the order of priority are limit, promo/discount, interest rate, and continued with weights of priorities are 0408, 0.28, 0.16, and 0.152. Keywords: AHP, Fuzzy Analytic Hierarchy Process (FAHP), Criteria of Credit Card, Consistensy Ratio , Weight Priority