Volatility plays an important role in the field of financial econometrics as one of the risk indicators. Many various models address the problem of modeling the volatilities of financial asset returns. This study provides a new empirical performance comparison of the four different GARCH-type models, namely GARCH, GARCH-M, GJR-GARCH, and log-GARCH models based on simulated data and real data such as the DJIA, S&P 500, and S&P CNX Nifty indices on a daily period from January 2000 to December 2017. We also investigate the estimation results obtained using Solver’Excel and verify those results against the results obtained using a Markov chain Monte Carlo method. The simulation study showed that the GARCH model is outperformed by other models. Meanwhile, the empirical study provides evidence that the GJR-GARCH model provides the best fitting, followed by the GARCH-M, GARCH, and log-GARCH models. Furthermore, this study recommends the use of Excel’s Solver in practice when the parameter estimates for GARCH-type model do not close to zero.

In the analysis of warranty, renewal functions are important in acquiring the expected number of failures of a nonrepairable component in a time interval. It is very difficult and complicated -if at all possible- to obtain a renewal function analytically. This paper proposes a numerical integration method for estimating renewal functions in the terms of renewal integral equations. The estimation is done through the Mean Value Theorem for Integrals (MeVTI) method after modifying the variable of the renewal integral equations. The accuracy of the estimation is measured by its comparison against the existing analytical approach of renewal functions, those are for Exponential, Erlang, Gamma, and Normal baseline failure distributions. The estimation of the renewal function for a Weibull baseline failure distribution as the results of the method is compared to that of the well-known numerical integration approaches, the Riemann-Stieljies and cubic spline methods. Keywords :    Mean Value Theorem for Integrals, Renewal Functions, Renewal Integral Equations.

The focus of this research is to analyze the production process queuing system at one of the stages of production of swiftlet nest in analytical and simulation. The purpose of this research is to obtain the model and characteristics of the queue system at the Finishing-2. The analysis uses data on the rate of arrival and the rate of service based on real observation and determines the probability distribution of data between arrival time and service time using the Easyfit 3.0 program, to get the model of the queuing system is obtained. After the model obtained, analytic and simulation analysis is carried out using the Queuing System Simulation (QSS) module in the WINQSB software. The results of the queuing system characteristics in the analytical and simulation have a significant difference, because the distribution of time between arrivals and service times used in analytical calculations is G (general), while the simulation uses a distribution that refers to a particular type of distribution according to the results of the Easyfit program. Simulation is carried out with the FIFO and SIRO queue disciplines. The simulation results show that 91% of the characteristics of the queue system in the two queue disciplines do not have a significant difference. Moreover, it has also been done a comparison between the characteristics of the queuing system in two different work areas namely Room A and Room B&C, based on the simulation results, the results show 58% of the characteristics of the queuing system have a significant difference, this is due to differences in service time between the two work areas. Thus the purpose of this research has been achieved which is obtained by the queue model (G/G/c):(FIFO/∞/∞), and also obtained system performance improvements, in the form of waiting time in the queue where the waiting time in Room B&C is smaller than Room A. Keywords: Queuing, Arrival, Service, Production, Simulation.

Abstrak: Analisis regresi adalah analisis yang sering digunakan dalam segala bidang yang bertujuan untuk memodelkan hubungan antara dua jenis variabel tak bebas dengan satu atau variabel bebas. Regresi linier masih memiliki beberapa kekurangan, maka dari untuk mengatasinya dengan regresi median. Copula dapat digunakan untuk mendeteksi hubungan data bivariat dengan peubah-peubah yang berbeda. Hasil penelitian menunjukkan kurva kuantil bersyarat terbaik berdasarkan MSE terkecil Data I yaitu copula Plackett sebesar 0.8650. Sedangkan nilai MSE terkecil Data II yaitu copula Gaussian sebesar 0.3954. Nilai MSE terkecil Data III yaitu copula Frank sebesar 0.5575. Terakhir, nilai MSE terkecil Data IV yaitu copula Clayton sebesar 0.3190.Abstract:  Regression analysis is an analysis that is often used in all fields which aims to model the relationship between two types of non-dependent variables with one or independent variables. Linear regression still has several drawbacks, so to overcome this by median regression. Copula can be used to detect bivariate data relations with different variables. The results showed that the best conditional curves based on the smallest MSE of Data I were Plackett copula of 0.8650. While the smallest MSE value is Data II, which is a Gaussian population of 0.3954. The smallest MSE value of Data III is Frank copula of 0.5575. Finally, the smallest MSE value is Data IV which is copula Clayton of 0.3190.

Pada masa sekarang ini film telah menjadi salah satu hiburan favorit utama masyarakat. Jumlah film pertahun terhitung mencapai ribuan. Hal ini membuat penggemar film kesulitan dalam memilih film mana yang tepat untuk ditonton sesuai keinginan. Sehingga dibutuhkan sistem rekomendasi yang bertujuan untuk memberikan saran film mana yang akan dipilih. Sistem rekomendasi adalah sistem yang membantu pengguna dalam mengatasi informasi yang meluap dengan memberikan rekomendasi spesifik bagi pengguna dan diharapkan rekomendasi tersebut bisa memenuhi keinginan dan kebutuhan pengguna. Terdapat tiga jenis sistem rekomendasi berdasarkan metode yang digunakannya yakni, collaborative filtering, content-based filtering, dan hybrid. Metode yang digunakan adalah collaborative filtering merupakan salah satu yang sering digunakan dalam sistem rekomendasi. Collaborative filtering dibagi menjadi dua bagian yaitu item-based collaborative filtering dan user-based collaborative filtering. Dalam tugas akhir ini penulis menggunakan metode item-based collaborative filtering. Data set yang digunakan adalah data set dari MovieLens.org berupa 100.000 rating yang diberikan oleh pengguna terhadap film. Data MovieLens akan diproses menggunakan program R dan memakai paket R yaitu recommenderlab.