Jurnal Matematika, Statistika dan Komputasi
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Forecasting Inflation In Indonesia Using The Modified Fuzzy Time Series Cheng
Get PDFInflation is one of the most important indicators to analyze a country’s economy. Therefore, it is necessary to forecast the inflation rate. Forecasting can be done by various methods, one of which is Fuzzy Time Series Cheng. In this study, several modifications were made to the method used. The purpose of this study is to forecast using the Modified Fuzzy Time Series (FTS) Cheng method and determine the accuracy of the forecasting results obtained. The results of this study indicate that the Modified FTS Cheng method can be used in forecasting, either by determining the interval average-based or using the Sturges equation. Based on the results of the calculation of forecasting accuracy using Mean Absolute Percentage Error (MAPE), the accuracy for Modified FTS Cheng by determining the average-based interval for forecasting based on the current state and next state is 11.58% and 5.78%, respectively. Furthermore, the Modified FTS Cheng by determining the interval using the Sturges equation resulted in a MAPE value of 9.61% and a FTS Cheng of 7.54%. The MAPE value of each method is less than 10%, which means that the method has a very good performance, except for Modified FTS Cheng by determining the average-based interval for forecasting based on current state has good performance with MAPE values between 10 % and 20%.
Inflasi merupakan salah satu indikator penting yang digunakan dalam menganalisa perekonomian di suatu negara. Oleh karena itu, perlu dilakukan peramalan terhadap tingkat inflasi. Peramalan dapat dilakukan dengan berbagai metode, salah satunya Fuzzy Time Series Cheng. Pada penelitian ini dilakukan beberapa modifikasi pada metode yang digunakan. Tujuan penelitian ini adalah melakukan peramalan menggunakan metode Fuzzy Time Series Cheng yang Dimodifikasi dan menentukan akurasi dari hasil peramalan yang diperoleh. Hasil dari penelitian ini menunjukkan bahwa metode Fuzzy Time Series Cheng Dimodifikasi dapat digunakan dalam melakukan peramalan, baik dengan penentuan interval berbasis rata-rata maupun menggunakan persamaan Sturges. Berdasarkan hasil perhitungan keakuratan peramalan menggunakan Mean Absolute Percentage Error (MAPE) diperoleh akurasi untuk Fuzzy Time Series Cheng Dimodifikasi dengan penentuan interval berbasis rata-rata untuk peramalan berdasarkan current state dan next state masing-masing sebesar 11,58% dan 5,78%. Selanjutnya, Fuzzy Time Series Cheng Dimodifikasi dengan penentuan interval meggunakan persamaan Sturges menghasilkan nilai MAPE sebesar 9,61% dan Fuzzy Time Series Cheng sebesar 7,54%. Nilai MAPE dari masing-masing metode kurang dari 10% yang berarti bahwa metode tersebut mempunyai kinerja yang sangat baik, kecuali Fuzzy Time Series Cheng Dimodifikasi dengan penentuan interval berbasis rata-rata untuk peramalan berdasarkan current state mempunyai kinerja yang baik dengan nilai MAPE berada antara 10% dan 20%
Forecasting Stock Price PT. Telkom Using Hybrid Time Series Regression Linear– Autoregressive Integrated Moving Average Model
Get PDFThe hybrid method is a method of combining two forecasting models. Hybrid method is used to improve forecasting accuracy. In this study, the Time Series Regression (TSR) linear model will be combined with the Autoregressive Integrated Moving Average (ARIMA) model. The TSR linear model is used to obtain the model and residual value, then the residual value of the TSR linear model will be modeled by the ARIMA model. This combination method will produce a hybrid TSR linear-ARIMA model. The case study in this research is stock closing price (daily) of PT. Telkom Indonesia Tbk. The stock closing price (daily) of PT. Telkom Indonesia Tbk in 2020 showed an decreasing and increasing trend pattern. The results of this study obtained the best model of hybrid TSR linear-ARIMA (2,1,1) with the proportion of data training and testing is 70:30. In the best model, the MAD value is 56.595, the MAPE value is 1.880%, and the RMSE value is 78.663. It is also found that the hybrid TSR linear-ARIMA model has a smaller error value than the TSR linear model. The results of forecasting the stock price of PT. Telkom Indonesia Tbk for the period 02 January 2021 to 29 January 2021 formed a decreasing trend pattern.Metode hybrid merupakan metode penggabungan dua model peramalan. Metode hybrid digunakana untuk meningkatkan akurasi peramalan.Pada penelitian ini, model Time Series Regression (TSR) linier akan digabungkan dengan model Autoregressive Integrated Moving Average (ARIMA). Model TSR linier digunakan untuk memperoleh model dan nilai residual, kemudian nilai residual dari model TSR linier akan dimodelkan oleh model ARIMA. Metode penggabungan ini akan menghasilkan model hybrid TSR linier-ARIMA. Studi kasus dalam penelitian ini adalah harga penutupan saham (harian) PT. Telkom Indonesia Tbk. Harga penutupan saham (harian) PT. Telkom Indonesia Tbk pada tahun 2020 menunjukkan pola trend turun dan trend naik. Hasil penelitian ini, diperoleh model terbaik hybrid TSR linier-ARIMA (2,1,1) dengan proporsi data in sample dan out sample adalah 70:30. Pada model terbaik, diperoleh nilai MAD sebesar 56,595, nilai MAPE sebesar 1,880%, dan nilai RMSE sebesar 78,663. Diperoleh juga bahwa model hybrid TSR linier-ARIMA memiliki nilai kesalahan yang lebih kecil dibandingkan dengan model TSR linier. Hasil peramalan harga saham PT. Telkom Indonesia Tbk periode 02 Januari 2021 sampai dengan 29 Januari 2021 membentuk pola trend turun
Solusi Primitif Persamaan Diophantine x^2+pqy^2=z^2 untuk bilangan-bilangan prima p dan q
No full textIn this paper, we determine the primitive solutions of diophantine equations x^2+pqy^2=z^2, for positive integers x, y, z, and primes p,q. This work is based on the development of the previous results, namely using the solutions of the Diophantine equation x^2+y^2=z^2, and looking at characteristics of the solutions of the Diophantine equation x^2+3y^2=z^2 and x^2+9y^2=z^2
Analisis Misklasifikasi Data Akreditasi Sekolah Dasar Di Kota Ambon Menggunakan Metode Multivariate Adaptive Regression Spline
Get PDFMany classification methods have been developed, one of which is the Multivariate Adaptive Regression Spline (MARS) method. MARS is one of the classification methods in the form of a combination of Recursive Partitioning Regression (RPR) and the spline method that is able to process high-dimensional and large-sized data and process data with continuous or binary response variables. The purpose of this study was to measure the misclassification of elementary school accreditation in Ambon city using the MARS method. This study uses accreditation data with the results of eight components of accreditation in elementary schools that have accreditation A (group 1) and accreditation B (group 2) in Ambon city. To evaluate the classification method used the APER classification error measure. The best classification result from the MARS method is when using a combination of BF=32, MI=3, MO=1 because it produces a minimum Generalized Cross Validation (GCV) of 0.066 and information is obtained that the correct classification data is 181 and the misclassified data is 10. Based on the results of the analysis, the size of the APER classification error is 5.23%, which can be said that the MARS method is good or statistically significant for classifying elementary schools in Ambon City based on their accreditation rating.
Metode klasifikasi telah banyak dikembangkan dimana salah satu diantaranya adalah metode Multivariate Adaptive Regression Spline (MARS). Tujuan penelitian ini adalah menganalisis misklasifikasi akreditasi Sekolah Dasar di kota Ambon dengan metode MARS. Penelitian ini menggunakan data akreditasi dengan hasil delapan komponen akreditasi di sekolah dasar yang memiliki akreditasi A (kelompok 1) dan akreditasi B (kelompok 2) di kota Ambon. Untuk mengevaluasi metode klasifikasi digunakan ukuran kesalahan klasifikasi APER. Hasil klasifikasi terbaik dari metode MARS adalah ketika menggunakan kombinasi BF=32, MI=3, MO=1 karena menghasilkan Generalized Cross Validation (GCV) minimum sebesar 0,066 dan diperoleh informasi bahwa data klasifikasi yang benar adalah 181 dan data yang salah klasifikasi adalah 10. Berdasarkan hasil analisis, diperoleh ukuran kesalahan klasifikasi APER sebesar 5,23% dimana dapat dikatakan bahwa metode MARS sudah baik atau signifikan secara statistik untuk mengklasifikasikan Sekolah Dasar di Kota Ambon berdasarkan peringkat akreditasinya
Regresi Binomial Negatif Bivariat untuk Pemodelan Kasus Konfirmasi dan Kasus Kematian akibat Covid-19 di Kalimantan
Get PDFCoronavirus disease (Covid-19) caused a pandemic severely affecting various sectors and paralyzed health services in Indonesia. As of June 2020, the percentage of Covid-19 confirmed cases in Kalimantan, the second largest island in Indonesia, contributed about 7% of the total national cases. In the same period, the percentage of Covid-19 deaths reached 12% of the national figure. This study used regression models to respond to bi-response count data consisting of Covid-19 confirmed cases and Covid-19 deaths in regencies/cities in Central Kalimantan and South Kalimantan provinces. This study compared the results of bivariate Poisson regression and bivariate negative binomial regression. There were thirteen predictors representing the determinants of health, social, economic, and demography indicators. The results showed that the prevalence of pneumonia had positive effect on Covid-19 confirmed cases and Covid-19 deaths. The percentage of elderly had negative effect on confirmed cases, while it had no significant effect on Covid-19 deaths. Bivariate negative binomial regression showed more satisfying performance on modeling Covid-19 cases and Covid-19 deaths jointly because it produced lower AIC and deviance than that of Poisson one. The negative bivariate model was also better than the Poisson one because it was able to overcome over-dispersion.
Coronavirus disease (Covid-19) menyebabkan pandemi yang berdampak parah pada berbagai sektor dan melumpuhkan pelayanan kesehatan di Indonesia. Pada akhir Juni 2020, persentase kasus konfirmasi Covid-19 di Kalimantan, pulau terbesar kedua di Indonesia, berkontribusi sekitar 7% dari total kasus nasional. Pada periode yang sama, persentase kasus kematian Covid-19 mencapai 12% dari angka nasional. Penelitian ini menggunakan model regresi untuk respon data cacah berganda yang terdiri atas kasus konfirmasi Covid-19 dan kasus kematian Covid-19 di kabupaten/kota pada Provinsi Kalimantan Tengah dan Provinsi Kalimantan Selatan. Penelitian ini membandingkan hasil pemodelan regresi Poisson bivariat dan regresi binomial negatif bivariat. Prediktor yang digunakan sebanyak tiga belas yang mewakili determinan dari indikator kesehatan, sosial, ekonomi, dan kependudukan. Hasil penelitian menunjukkan bahwa prevalensi pneumonia berpengaruh positif pada kasus konfirmasi dan kasus kematian Covid-19. Adapun persentase lansia berpengaruh negatif pada kasus konfirmasi, dan tidak signifikan berpengaruh pada kasus kematian Covid-19. Regresi binomial negatif bivariat menunjukkan kinerja yang lebih memuaskan dalam memodelkan kasus konfirmasi Covid-19 dan kasus kematian Covid-19 secara bersama karena menghasilkan AIC dan devians yang lebih rendah ketimbang regresi Poisson. Model bivariat negatif juga lebih baik daripada model Poisson karena mampu mengatasi over-dispersi
Shifted Liu-Type Estimator in The Linear Regression
Get PDFThe methods to solve the problem of multicollinearity have an important issue in the linear regression. The Liu-type estimator is one of these methods used to reduce its effect. This estimator is an estimator with two parameters denoted and . Kurnaz and Akay (2015) [6] introduced a new approach for the Liu-type estimator and called it new Liu-type (NL) estimator. This proposed estimator is based on a continuous function of rather than two parameters and includes OLS, ridge estimator, Liu estimator, and some estimators with two biasing parameters as special cases. This study aimed to improve the NL estimator by shifting. The performance of the shifted NL estimator is compared to the NL estimator and other estimators depending on the mean squared error (MSE) criterion. The real data example and simulation study reveal that the SNL estimator can be a good selection in the linear regression model
New Mathematical Properties For Rayleigh distribution
Get PDFRegression analysis is one of the most commonly statistical techniques used for analyzing data in different fields. And used to fit the relation between the dependent variable and the independent variables require strong assumption to be met in the model. Generalized linear models (GLMs) allow the extension of linear modeling ideas to a wider class of response types, such as count data or binary responses. Many statistical methods exist for such data types, but the advantage of the GLM approach is that it unites a seemingly disparate collection of response types under a common modeling methodology. So, the problem of the current research is to try to provide a new mathematical property for Exponentiated Rayleigh distribution, and it was one of the most important properties that was studied is to determine Harmonic Mean, as well as calculating the Quantile function, Moments of Residual life (MRL), Reversed Residual Life, Mean of Residual life. The study also presented the probability density function (pdf) and cumulative distribution function according to linear representations.
Clustering Regencies/Cities in Kalimantan Island Based on Poverty Indicators using Agglomerative Hierarchical Clustering (AHC)
Get PDFCluster analysis is a statistical analysis that can group objects of observation into several groups/clusters based on their similarity of characteristics. The grouping into several clusters is based on the information contained in the object under study. A cluster can be said to be good if it has high internal homogeneity and high external heterogeneity. The clustering method used in this study is the agglomerate hierarchical clustering (AHC) method, where the cluster formation algorithm used in this AHC method is average linkage, single linkage, complete linkage, and ward. Cluster analysis using the AHC method will be applied to poverty indicator data for Regencies/Cities in Kalimantan Island, which consists of several variables. This study aims to obtain the optimal results of grouping Regencies/Cities in Kalimantan Island, with the number of clusters that have been determined at the beginning, namely as many as 3 clusters. Based on the results of the analysis using the AHC method, the ward algorithm produces an agglomerate coefficient value of 0.89, where this value is close to 1, which means that the ward algorithm is the best in clustering Regencies/Cities in Kalimantan Island
Comparison of Variance Covariance and Historical Simulation Methods to Calculate Value At Risk on Banking Stock Portfolio
Get PDFIn investing, all investors must be faced with risk that must be borne. Therefore, to determine the best strategy in investing, every investor must calculate the risk. One statistical approach that can be used to measure the risk is Value at Risk (VaR). VaR is defined as a tolerable loss with a certain level of confidence. The purpose of this research is to estimate VaR using Variance Covariance and Historical Simulation methods on banking stock portfolio consisting of three stocks for the period 11 September 2020-30 September 2021. Both methods will then be evaluated using backtesting to determine the accuracy of VaR and to obtain the best method. From the research results, if the holding period is 1 day, then the VaR calculation for banking stock portfolio using both methods can be used to estimate the risk at 99% and 95% confidence levels, except for the VaR value using the Variance Covariance method for banking stock portfolio at 95% confidence level. The results show that Variance Covariance method is the best method for 99% confidence level. As for the 95% confidence level, Historical Simulation method is the best method
Geographically Weighted Poisson Regression Model with Adaptive Bisquare Weighting Function (Case study: data on number of leprosy cases in Indonesia 2020)
Get PDFAbstract
Geographically Weighted Poisson Regression (GWPR) is a Poisson regression model which is applied on spatial data. The parameter estimation of GWPR is done in each observation location through spatial weighting. This study aims to determine the GWPR model of the number of leprosy cases in each province of Indonesia 2020 and to find the influencing factors. The research uses secondary data collected from Indonesian Ministry of Health and Central Statistics Agency. The spatial weighting is calculated by using the adaptive bisquare function, while the optimum bandwidth is determined by using Generalized Cross-Validation criteria (GCV). The parameter estimation of GWPR uses Maximum Likelihood Estimation (MLE) method. The result of research show that the closed form of Maximum Likelihood (ML) estimator can not be found analytically and that the approximation of ML estimator is found by using Newton-Raphson iterative method. Based on the parameter significance test of the GWPR model, the factors that influenced the number of leprosy cases locally are the percentage of households that have access to proper sanitation, population density, the percentage of people who experience health complaints and outpatient, the number of health workers, the percentage of poor people, the percentage of districts/cities that carry out healthy living community movement (GERMAS) and the percentage of habitable houses. While the factors that globally affected the number of leprosy cases are the percentage of households that have access to proper sanitation, population density, the percentage of people who experience health complaints and outpatient, the number of health workers, the percentage of poor people, the percentage of districts/cities that carry out GERMAS.
Abstrak
Model Geographically Weighted Poisson Regression (GWPR) adalah model regresi Poisson yang diaplikasikan pada data spasial. Penaksiran parameter model GWPR dilakukan pada setiap lokasi pengamatan menggunakan pembobot spasial. Tujuan penelitian ini adalah menentukan model GWPR data jumlah kasus kusta di setiap provinsi di Indonesia tahun 2020 dan untuk mengetahui faktor-faktor yang memengaruhinya. Data penelitian adalah data sekunder diperoleh dari Kementerian Kesehatan Indonesia dan Badan Pusat Statistik. Pembobot spasial diperoleh menggunakan fungsi kernel adaptive bisquare dan bandwidth optimum ditentukan menggunakan kriteria Generalized Cross-Validation (GCV). Metode penaksiran parameter model GWPR adalah Maximum Likelihood Estimation (MLE). Hasil penelitian menunjukkan bahwa penaksir eksak Maximum Likelihood (ML) tidak dapat diperoleh secara analitik dan hampiran penaksir ML didapat menggunakan metode iteratif Newton-Raphson. Berdasarkan hasil pengujian parameter model GWPR, disimpulkan bahwa faktor-faktor yang berpengaruh secara lokal adalah persentase rumah tangga yang memiliki akses sanitasi layak, kepadatan penduduk, persentase penduduk yang mengalami keluhan kesehatan dan berobat jalan, jumlah tenaga kesehatan, persentase penduduk miskin, persentase kabupaten/kota yang melaksanakan GERMAS dan persentase rumah layak huni. Faktor-faktor yang berpengaruh secara global adalah persentase rumah tangga yang memiliki akses sanitasi layak, kepadatan penduduk, persentase penduduk yang mengalami keluhan kesehatan dan berobat jalan, jumlah tenaga kesehatan, persentase penduduk miskin, persentase kabupaten/kota yang melaksanakan GERMAS. Berdasarkan pendeteksian parameter dispersi diperoleh nilai parameter dispersi model GWPR sebesar 12,0322 lebih kecil dari parameter dispersi model global (yaitu sebesar 694,3697). Pemodelan GWPR pada kasus kusta penelitian ini belum memenuhi asumsi equidispersi.
Kata kunci: Adaptive Bisquare, GCV, GWPR, Overdispersi, Kust