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Jurnal Gaussian

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Published by Universitas Diponegoro

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Jurnal Gaussian terbit 4 (empat) kali dalam setahun setiap kali periode wisuda. Jurnal ini memuat tulisan ilmiah tentang hasil-hasil penelitian, kajian ilmiah, analisis dan pemecahan permasalahan yang berkaitan dengan Statistika yang berasal dari skripsi mahasiswa S1 Departemen Statistika FSM UNDIP.

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Articles 733 Documents

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VALUASI KUPON OBLIGASI PT. BPD LAMPUNG TBK. MENGGUNAKAN OPSI MAJEMUK CALL ON CALL TIPE EROPA Revaldo Mario; Diah Safitri; Agus Rusgiyono
Jurnal Gaussian Vol 5, No 2 (2016): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

A bond is a debt capital market instrument issued by a borrower, who is then required to repay to the lender/investor the amount borrowed plus interest at maturity, and also known as fixed-income securities, and therefore the bond is an attractive investment in the financial sector. Most theories about the financial statistics is based on the bond without coupon bonds. Whereas, in fact most companies issue bonds with a coupon. Option is an agreement or contract which provides the right and not an obligation for the holder of a contract to buy (call option) or sell (put option) a particular asset at a price and time have been set. Underlying assets can be stocks, bonds, warrants and more. One type of option trading is a European type option is an option that can be used only at the time of maturity. The approach used in the valuation of bond coupons is to use the theory of Europe style compound option call on call. European style compound option call on call is the type of European call options with underlying assets are call options. Final project aims to get the value of equity and the value of liabilities on the bonds PT BPD Lampung Tbk with a coupon rate when the bond before maturity (compound option strike price) and a coupon rate of the bond at maturity (the strike price of the call option). The current bond coupon payments prior to maturity was conducted on July 9, 2017 and a coupon payment at maturity conducted on 9 October 2017. Based on the results of data processing with the help of open source software R 3.1.1, the value of the equity is greater than the value of liabilities.Keywords: bond, call option, compound option, coupon bond, equity, liability

ANALISIS SEKTOR UNGGULAN MENGGUNAKAN DATA PDRB (Studi Kasus BPS Kabupaten Kendal Tahun 2006-2010) Rosita Wahyuningtyas; Agus Rusgiyono; Yuciana Wilandari
Jurnal Gaussian Vol 2, No 3 (2013): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Gross Domestic Regional Product (GDRP) is total numbers of added values who’s producting by effort unit in that domestic area’s. GDRP can be classified in two form, that is GRDP at Current Market Prices and GRDP at Constant Prices. GRDP at Current Market Prices is calculating with two approaches, those are approach production and approach income. GRDP at Constant Prices can be calculated using two methods, revaluation and deflation. By using GDRP data, then it can be known which sector is prominent sector in that region. Some methods who using GDRP data as decisive prominent sector is method of Typology Klassen, LQ, MRP, Overlay and Shift Share. These methods classifying the economic sectors into four groups, they are prominent sector, growing sector, potential sector and under developed sector, based on large of contribution and rate of growth. By taking the study area Kendal Regency and reference area is province Central of Java, then by used that methods can be known which sector be prominent sector in Kendal Regency. Based on the result from analysis methods, they are same result about prominent sector: agriculture sector and mining and quarrying sector

PEMODELAN RETURN HARGA SAHAM MENGGUNAKAN MODEL INTERVENSI–ARCH/GARCH (Studi Kasus : Return Harga Saham PT Bayan Resources Tbk) Dea Manuella Widodo; Sudarno Sudarno; Abdul Hoyyi
Jurnal Gaussian Vol 7, No 2 (2018): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

The intervention method is a time series model which could be used to model data with extreme fluctuation whether up or down. Stock price return tend to have extreme fluctuation which is caused by internal or external factors. There are two kinds of intervention function; a step function and a pulse function. A step function is used for a long-term intervention, while a pulse function is used for a short-term intervention. Modelling a time series data needs to satisfy the homoscedasticity assumptions (variance of residual is homogeneous). In reality, stock price return has a high volatility, in other words it has a non-constant variance of residuals (heteroscedasticity). ARCH (Autoregressive Conditional Heteroscedasticity) or GARCH (Generalized Autoregressive Conditional Heteroscedasticity) can be used to model data with heteroscedasticity. The data used is stock price return from August 2008 until September 2018. From the stock price return data plot is found an extreme fluctuation in September 2017 (T=110) that is suspected as a pulse function. The best model uses the intervention pulse function is ARMA([1,4],0) (b=0, s=1, r=1). The intervention model has a non-constant variance or there is an ARCH effect. The best variance model obtained is ARMA([1,4],0)(b=0, s=1, r=1)–GARCH(1,1) with the AIC value is -205,75088. Keywords: Stock Return, Intervention, Heteroscedasticity, ARCH/GARCH

ANALISIS KINERJA PORTOFOLIO OPTIMAL CAPITAL ASSET PRICING MODEL (CAPM) DAN MODEL BLACK LITTERMAN Anton Suhartono; Sugito Sugito; Rita Rahmawati
Jurnal Gaussian Vol 4, No 3 (2015): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Stock portfolio is investment which comprised of various stocks from different companies, with the hope when the price of one stock decreases, while the other increases, investments do not suffer losses.The final stage in the investment process is to assess the performance of a portfolio. The purpose of portfolio performance assessment is to determine and analyze whether the formed portfolio have a better performance than other portfolios. Capital Asset Pricing Model (CAPM) explains that historical data and unrisk asset are used to to form portfolio. Black Litterman modelis developed by Robert Litterman and Fisher Black in the 1990s, forming a portfolio by combining historical data and investor intuition or investor views about the economic conditions that are happening. CAPM portfolio and Black Litterman model portfolio performance assessment can be performed by using Sharpe index, Treynor index and Jensen index. This research uses data from closing prices of stocks that join BISNIS-27 Index on period January 2010 until December 2014. Based on Sharpe index, Treynor index and Jensen index, optimal portfolio is CAPM portfolio with consisted by two stocks and the proportion investement are 86.936% for BMRI and 13.064% for INCO. Keywords: BISNIS-27 Index, Portfolio, Capital Asset Pricing Model (CAPM), Black Litterman Model, Treynor Index, Sharpe Index, Jensen Index.

PEMODELAN MARKOV SWITCHING DENGAN TIME-VARYING TRANSITION PROBABILITY Anggita Puri Savitri; Budi Warsito; Rita Rahmawati
Jurnal Gaussian Vol 5, No 4 (2016): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Exchange rate or currency is an economic variable which reflects country’s state of economy. It fluctuates over time because of its ability to switch the condition or regime caused by economic and political factors. The changes in the exchange rate are depreciation and appreciation. Therefore, it could be modeled using Markov Switching with Time-Varying Transition Probability which observe the conditional changes and use information variable. From this model, time-varying transition probability and expected durations are obtained; both are very useful to explain economic growth better and more detailed. This research modeled ln return value of Indonesian Rupiah to U.S Dollars and using ln return value of Indonesian Rupiah to Euro as information variable. The best model is MS(2) – AR(1). Overall, the mean of transition probability from appreciation to depreciation is 0,025242 and the transition probability from depreciation to appreciation is 0,666369. Expected duration of appreciation is 39,61623 days meanwhile the expected duration of depreciation is 39,18689 days. Keywords : regime switching, Markov switching, time-varying, transition probability, expected duration

ANALISIS GRAFIK PENGENDALI NONPARAMETRIK DENGAN ESTIMASI FUNGSI DENSITAS KERNEL PADA KASUS WAKTU PELOROTAN BATIK TULIS Hana Hayati; Rukun Santoso; Agus Rusgiyono
Jurnal Gaussian Vol 3, No 1 (2014): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

The quality of the product becomes one of the basic factors in the decisions of consumers in selecting products. A companny needs a quality control for keeping the consistency of product quality. One of statistic tools which can be used in quality control is a control chart. If the obtained data do not have a specific distribution assumption, it is needs to use nonparametric control chart as the solution. One of ways to describe the nonparametric control chart is a kernel density estimation. The most important point in the kernel density estimation is optimal bandwidth selection and one of the method that can be used is Least Squares Cross Validation. In this case, will be described a nonparametric control chart to data of vanishing candle at batik in Pekalongan using Rectangular, Triangular, Biweight and Epanechnikov kernel density estimation. Based on the data processing using R.2.14, the result was obtained that from the four kernel estimatios which were used, the obtained control chart by the Rectangular kernel density estimation which have the largest value of variance. It shows that the control chart by the Rectangular kernel density estimation is the widest control chart. While, the obtained control chart by the Epanechnikov kernel density estimation which have the smallest value of variance. It shows that the control chart by the Epanechnikov kernel density estimation is the narrowest control chart

PEMILIHAN PERUMAHAN TERFAVORIT MENGGUNAKAN METODE VIKOR DAN TOPSIS DENGAN GUI MATLAB (Studi Kasus: Perumahan Mijen Semarang) Alika Ramadhani; Rukun Santoso; Rita Rahmawati
Jurnal Gaussian Vol 8, No 3 (2019): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

The increase in the population of Semarang has an impact on the increasing demand for residential housing. Unfortunately, the limitations of the area became an obstacle in Semarang to develop residential areas. This development of residential housing in Semarang leads to suburban such as Mijen. The method that can be used to choose favorite housing is Visekriterijumsko Kompromisno Rangiranje (VIKOR) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Both methods can be applied to solve Multiple Criteria Decision Making (MCDM) issue. This study has 8 alternatives of residential housing in Mijen with 5 criteria such as Price, Payment Method, Building Specifications, Housing Facilities, and Location. This research was design with Graphical User Interface (GUI) Matrix Laboratory (MATLAB) as computing tool. VIKOR and TOPSIS method on this research, obtained the same result that the most favorite residential housing is A5. Keywords: Housing, SPK, VIKOR, TOPSIS, GUI

PENGUKURAN PROBABILITAS KEBANGKRUTAN OBLIGASI PERUSAHAAN DENGAN MODEL FIRST PASSAGE TIME Amalia Diwati; Di Asih I Maruddani; Abdul Hoyyi
Jurnal Gaussian Vol 1, No 1 (2012): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Salah satu akibat dari kegiatan investasi adalah risiko kredit. Risiko kredit ialah risiko kerugian yang berhubungan dengan probabilitas counterparty gagal memenuhi kewajibannya pada saat jatuh tempo. Ada dua permodelan utama dalam analisis risiko kredit yaitu model struktural dan model tereduksi. Model First Passage Time merupakan salah satu model struktural yang diperkenalkan oleh Black dan Cox (1976). Model ini merupakan pengembangan model dasar Merton yang mengasumsikan bahwa kebangkrutan perusahaan dapat terjadi kapanpun, saat awal penerbitan hingga jatuh tempo, ketika nilai aset perusahaan berada di bawah nilai obligasi perusahaan. Studi empiris dilakukan pada data obligasi dan aset PT Bank Lampung Tbk periode November 2004 sampai dengan Januari 2012. Berdasarkan output pemrograman R, diperoleh nilai probabilitas kebangkrutan sebesar 0.002121936% dan nilai pasar ekuitas sebesar Rp 2.127.054.000.000,00.

PENERAPAN MODEL INDEKS TUNGGAL UNTUK OPTIMALISASI PORTOFOLIO DAN PENGUKURAN VALUE AT RISK DENGAN VARIANCE COVARIANCE (Studi Kasus: Saham yang Stabil dalam LQ 45 Selama Periode Februari 2011 – Juli 2016) Hanifa Eka Oktafiani; Di Asih I Maruddani; Suparti Suparti
Jurnal Gaussian Vol 6, No 1 (2017): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

One of popular investments among investors is investing in a form of stock in go public companies. Investing stocks must not be separated from a wide variety of risks. One way to minimize risk is by taking a portfolio of several stocks. This research uses single index model to form portfolio of several stocks because it has simple computation than other method. This model based on the observation that price of securities have linier fluctuation with market indeks. Estimate of Value at Risk (VaR) can be calculated using variance covariance method which requires that return of a stock and return portfolio of several stocks have a normal distribution. This research aplicated to stable several stocks, in the meaning that always recorded in LQ 45 during February 2011 until July 2016. Based on 21 stable stocks in LQ 45, there are six stocks included in the optimal portfolio. That is stock of GGRM (Gudang Garam Ltd.), BBCA (Bank Central Asia Ltd.), JSMR (Jasa Marga Persero Ltd.), LPKR (Lippo Karawaci Ltd.), BBRI (Bank Rakyat Indonesia Persero Ltd.), and INDF (Indofood Sukses Makmur Ltd.), which estimated of VaR in a month after investing on optimal portfolio at 95% confidence level is Rp 7.846.572,00 from initial capital of Rp 100.000.000,00. Keywords: Portfolio, Stock, Single Index Model, Variance Covariance, LQ 45

IDENTIFIKASI CURAH HUJAN EKSTREM DI KOTA SEMARANG MENGGUNAKAN ESTIMASI PARAMETER MOMEN PROBABILITAS TERBOBOTI PADA NILAI EKSTREM TERAMPAT (Studi Kasus Data Curah Hujan Dasarian Kota Semarang Tahun 1990-2013) Annisa Rahmawati; Agus Rusgiyono; Triastuti Wuryandari
Jurnal Gaussian Vol 3, No 4 (2014): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

The methods used to analyze extreme rainfall is the Extreme Value Theory (EVT). One of the approaches of EVT is the Block Maxima (BM) which follows the distribution of Generalized Extreme Value (GEV). In this study, the dasarian rainfall data of 1990-2013 in the Semarang City is divided based on block monthly and the month examined are October, November, December, January, February, March and April. The resulted blocks are 24 with 3 observations each block. Estimated parameter of form, location and scale are obtained by using the method of Probability Weight Moments (PWM). The result of this study is January has the greatest occurrence chance of extreme value with the value of estimated parameter of form 0,3840564, location 138,8152989 and scale 68,6067117. In addition, the alleged maximum value of dasarian rainfall obtained in a period of 2, 3, 4, 5 and 6 years are 243,45753 mm, 308,23559 mm, 357,26996 mm, 397,96557 mm and 433,28889 mm. Keywords: rainfall, Extreme Value Theory, Block Maxima, Generalized Extreme Value, Probability Weight Moments

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