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UJI STASIONERITAS DATA INFLASI DENGAN PHILLIPS-PERON TEST Maruddani, Di Asih I; Tarno, Tarno; Anisah, Rokhma Al
MEDIA STATISTIKA Vol 1, No 1 (2008): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (71.414 KB) | DOI: 10.14710/medstat.1.1.27-34

Abstract

The classical regression model was devised to handle relationships between stationary variables. It should not be applied to nonstationary series. A time series is therefore said to be stationary is its mean, variance, and covariances remain constant over time. A problem associated with nonstationary variables, and frequently faced by econometricians when dealing with time series data, is the spurious regression. An apparent indicator of such spurious regression was a particularly low level for the Durbin-Watson statistics, combined with an acceptable R2. Statistical test for stationarity have proposed by Dickey and Fuller (1979). The distribution theory supporting the Dickey-Fuller test assumes that the errors are statistically independent and have a constant variance. Phillips and Peron (1988) developed a generalization of the Dickey-Fuller procedure that the error terms are correlated and not have constant variance. In this paper, we use Phillips-Peron test for inflation data in Indonesia for the time period 1996-2003. The data showed upward trend and the error terms are correlated. The empirical results showed that the inflation data in Indonesia is a nonstationary series.   Keywords : stationarity, non autocorrelation, Phillips-Peron Test, inflation
PEMILIHAN THRESHOLD OPTIMAL PADA ESTIMATOR REGRESI WAVELET THRESHOLDING DENGAN METODE CROSS VALIDASI Suparti, Suparti; Tarno, Tarno; Hapsari, Paula Meilina Dwi
MEDIA STATISTIKA Vol 2, No 2 (2009): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (341.567 KB) | DOI: 10.14710/medstat.2.2.56-69

Abstract

If x is a predictor variable and y is a response  variable of  the regression model y = f (x)+ Î with  f is a regression function which not yet been known and Î is independent random variable with mean 0 and variance , hence function f can be estimated by parametric and nonparametric approach. In this paper function f is estimated with a nonparametric approach. Nonparametric approach that used is a wavelet shrinkage or a wavelet threshold method. In the function estimation with a wavelet threshold method,  the value of  threshold has  the most important role to determine  level of smoothing estimator. The small threshold give function estimation very no smoothly, while  the big value of threshold give function estimation very smoothly. Therefore the optimal value of threshold should be selected to determine the optimal function estimation. One of the methods to determine the optimal value of threshold by minimize a cross validation function. The cross validation method that be used is two-fold cross validatiaon. In this cross validation, it compute the predicted value by using a half of data set. The original data set is split  into two subsets of equal size : one containing only the even indexed data, and the other, the odd indexed data. The odd data will be used to predict the even data, and vice versa. Based on  the result of data analysis, the optimal threshold with cross validation method is not uniq, but they give the  uniq of wavelet thersholding regression estimation.   Keywords : Nonparametric Regression, Wavelet Threshold Estimator, Cross Validation.
PEMILIHAN PARAMETER THRESHOLD OPTIMAL DALAM ESTIMATOR REGRESI WAVELET THRESHOLDING DENGAN PROSEDUR FALSE DISCOVERY RATE (FDR) Suparti, Suparti; Tarno, Tarno; Haryono, Yon
MEDIA STATISTIKA Vol 1, No 1 (2008): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (235.567 KB) | DOI: 10.14710/medstat.1.1.1-9

Abstract

If X is predictor variable and Y is response  variable of following model Y = f (X) +e with function f is regression which not yet been known and e is independent random variable with mean 0 and variant , hence function of f can estimate with parametric and nonparametric approach. At this paper estimate f with nonparametric approach. Nonparametric approach that used is wavelet shrinkage or wavelet thresholding method. At function estimation with method of wavelet thresholding, what most dominant determine level of smoothing estimator is value of threshold. The small threshold give function estimation very no smoothly, while  the big value of threshold give function estimation very smoothly. Therefore require to be selected value of optimal threshold to determine optimal function estimation.               One of the method to determine the value of optimal threshold is with procedure of False Discovery Rate ( FDR). In procedure of FDR, the optimal threshold determined by selection of level of significance. Smaller mount used significance progressively smoothly its .   Keywords: Nonparametric regression, wavelet thresholding estimator, procedure of False Discovery Rate
ESTIMASI MODEL UNTUK DATA DEPENDEN DENGAN METODE CROSS VALIDATION Tarno, Tarno
MEDIA STATISTIKA Vol 1, No 2 (2008): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (127.66 KB) | DOI: 10.14710/medstat.1.2.75-82

Abstract

This paper discuss about application of cross-validation method for modeling of dependent data. One of the data that categorized into dependent data is a time series. To construct the mathematical model for a time series data, we must have at least 50 series. In practices we often have some problem as long as we collect the time series data. So we don’t get ideal data related to number of sample. To solve this problem, we can generate observation data. There are several methods that can be used to generate data such as cross-validation and bootstrap. Application of cross-validation method to generate time series data can’t be done randomly, but we must generate the data based on balanced incomplete block design. The basic principle of cross-validation method is the data divided into two parts those are construction data and validation data. Construction data are drawn from observation data based on moving block and then we construct the model with Box-Jenkins method and verify the model with validation data. Do this process for different blocks as replication samples of cross-validation method, such that we can construct the best model that minimized loss function for prediction errors.   Key words: time series data, estimate model, cross-validation
PEMODELAN DATA INFLASI INDONESIA PADA SEKTOR TRANSPORTASI, KOMUNIKASI, DAN JASA KEUANGAN MENGGUNAKAN METODE KERNEL DAN SPLINE Suparti, Suparti; Tarno, Tarno
MEDIA STATISTIKA Vol 8, No 2 (2015): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (249.852 KB) | DOI: 10.14710/medstat.8.2.103-110

Abstract

In this research, we study data modeling of Indonesian inflation in the  transportation, communication and financial services sector using the kernel and spline models. Determination of the optimal models based on the smallest of GCV  value and determination of the best model based on the smallest out sampels of Mean Square Error (MSE) value. By modeling the yoy (year on year) inflation data in Indonesia in the transportation, communication and financial services sector In January 2007 to January 2015, shows that the kernel model  using Gaussian kernel function obtained optimal model with a bandwidth  0.24 and the optimal spline model with order 5 and  4 points knots. Based on out sampels data  in February to August 2015, obtained out sampels  MSE value of the spline model is smaller than the kernel model. So that the spline model is better than the kernel model  to analyze  the inflation data  of transportation, communication and financial services sector.Keywords: Inflation, Transportation, Communication and Financial Services Sector, Kernel, Spline, GCV, MSE.
PEMILIHAN MODEL REGRESI LINIER DENGAN BOOTSTRAP tarno, Tarno; subanar, subanar
MATEMATIKA Vol 4, No 1 (2001): JURNAL MATEMATIKA
Publisher : MATEMATIKA

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (97.669 KB)

Abstract

Tulisan ini membicarakan tentang penerapan bootstrap untuk pemilihan model regresi linier terbaik. Model regresi linier terbaik yang terpilih adalah model dengan estimasi sesatan prediksi kuadrat minimal atas semua model regresi  yang mungkin yaitu sebanyak 2p-1 model dengan p: banyaknya variabel prediktor. Metode Bootstrap memilih suatu model dengan meminimalkan rata-rata sesatan prediksi kuadrat berdasarkan  resampling data yang dibangkitkan melalui pasangan data dan residual, dengan mempertimbangkan juga variabel prediktor yang terlibat sesedikit mungkin. Pemilihan variabel berdasarkan bootstrap pasangan data dan bootstrap residual dengan n ukuran sampel bootstrap adalah konsisten. Dan jika ukuran sampel bootstrap diambil m dengan , pemilihan variabel bootstrap juga konsisten. Hasil dari suatu simulasi dengan SPLUS disajikan dalam tulisan ini.  
Estimasi Model Regresi Linier Dengan Metode Median Kuadrat Terkecil Tarno, Tarno
JURNAL SAINS DAN MATEMATIKA Volume 15 Issue 2 Year 2007
Publisher : JURNAL SAINS DAN MATEMATIKA

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (500.739 KB)

Abstract

ABSTRAK---Model regresi linier merupakan model yang paling sering digunakan dalam analisis statistika. Model regresi linier ini digunakan untuk menyatakan hubungan fungsional antara satu atau beberapa variabel bebas (prediktor) terhadap satu variabel terikat (respon). Dalam analisis regresi, mengestimasi parameter secara otomatis mengestimasi model regresi. Untuk memperoleh estimasi model regresi dapat dilakukan dengan beberapa metode antara lain: metode kuadrat terkecil, metode maksimum likelihood dan sebagainya. Salah satu metode yang paling populer adalah metode kuadrat terkecil (OLS). Pada prinsipnya metode kuadrat terkecil mengestimasi model regresi dengan meminimalkan rata-rata kuadrat sesatan (MSE). Dalam tulisan ini dibahas suatu metode alternatif untuk mendapatkan estimasi model regresi yaitu metode median kuadrat terkecil (LMS). Pada metode LMS, estimasi model yang diperoleh adalah suatu model yang memiliki median kuadrat sesatan terkecil. Prosedur estimasinya adalah dengan memilih p titik sampel (dengan p: banyaknya parameter di dalam model termasuk intersept) dari n titik sampel hasil pengamatan, kemudian ditentukan suatu persamaan yang melalui p titik tersebut. Setelah diperoleh sejumlah persamaan yang melalui p titik tersebut, kemudian ditentukan median dari residual kuadrat. Persamaan atau model yang diestimasi melalui p titik yang menghasilkan nilai median kuadrat terkecil merupakan model yang terpilih.   Kata Kunci: regresi linier, estimasi parameter, sesatan kuadrat
MODEL KOMBINASI ARIMA DALAM PERAMALAN HARGA MINYAK MENTAH DUNIA Setiyowati, Eka; Rusgiyono, Agus; Tarno, Tarno
Jurnal Gaussian Vol 7, No 1 (2018): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (455.014 KB) | DOI: 10.14710/j.gauss.v7i1.26635

Abstract

Oil is the most important commodity in everyday life, because oil is one of the main sources of energy that is needed for other people. Changes in crude oil prices greatly affect the economic conditions of a country.  Therefore, the aim of this study is develop an appropriate model for forecasting crude oil price based on the ARIMA and its ensembles. In this study, ensemble method uses some ARIMA models to create ensemble members which are then combined with averaging and stacking techniques. The data used are the price of world crude oil period 2003-2017. The results showed that ARIMA (1,1,0) model produces the smallest RMSE values for forecasting the next thirty six months. Keywords: Ensemble, ARIMA, Averaging, Stacking, Crude Oil Price
PERAMALAN JUMLAH WISATAWAN YANG BERKUNJUNG KE OBJEK WISATA DI JAWA TENGAH MENGGUNAKAN VARIASI KALENDER ISLAM REGARIMA Jesica, Haniela Puja; Ispriyanti, Dwi; Tarno, Tarno
Jurnal Gaussian Vol 8, No 3 (2019): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (492.107 KB) | DOI: 10.14710/j.gauss.v8i3.26676

Abstract

Tourism is one of the most strategically controlled areas that have been developed.The number of tourists in Central Java is constantly rising in the month of Eid Al-Fitr caused by holiday and mudik to hometown. The shift of the Eid Al-Fitr month on the data will form a seasonal pattern with an unequal period, then called moving holiday effect.One of the calendar variationsare often used to remove the moving holiday effect is RegARIMA model. RegARIMA is a combination of the linier regression and ARIMA, which a weight was used as a regression variable and error of regression model was used a variable in the ARIMA process. Based on the analysis carried out on the monthly number of tourists visiting tourist attractions in Central Java data for the period January 2011 to December 2017, the RegARIMA (1,1,1) (0,0,1)12model as the best model because it have the lowest AIC value than other model. The forecasting results in 2018 shows an increase on number of tourists data on June 2018 which coincided with the Eid Al-Fitr holiday on 15 June 2018. sMAPE value is 23,298%.Keyowrds:Time Series, Tourists, RegARIMA, Moving Holiday Effect
PEMILIHAN INPUT MODEL REGRESSION ADAPTIVE NEURO FUZZY INFERENCE SYSTEM (RANFIS) UNTUK KAJIAN DATA IHSG Sari, Sasmita Kartika; Tarno, Tarno; Safitri, Diah
Jurnal Gaussian Vol 6, No 3 (2017): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (455.733 KB) | DOI: 10.14710/j.gauss.v6i3.19348

Abstract

The Jakarta Composite Index (JCI) is one of indexes issued by the Indonesia Stock Exchange (IDX) with its calculation component using all the registered emiten. Several factors affecting the JCI are Dow Jones Index, inflation, and USD/IDR exchange rate. The study used Regression Adaptive Neuro Fuzzy Inference System (RANFIS) to analyze the affect of predictor variables on the JCI. The role of regression in RANFIS is a preprocessing in the determination of input in ANFIS. The optimum ANFIS model in RANFIS is strongly influenced by three things, they are input determination, membership functions, and rule. The technique of defining rules followed the rule of genfis1 and genfis3. The model accuracy was measured using the smallest RMSE and MAPE. Based on the empirical studies which implemented Dow Jones Index, inflation, and USD/IDR exchange rate as the predictors and JCI as the response, it was obtained that optimum RANFIS model with gauss membership function, the number of cluster 2 with 2 rules generated by genfis3 produced RMSE in-sample 233.0 and out-sample 301.9, as well as MAPE in-sample 6.5% and out-sample 4.8%. While in regression analysis, it obtained RMSE in-sample 351.27 and out-sample 590.99, as well as MAPE in-sample 9.6% and out-sample 10.2% with violation of assumption. This shows that the result of RANFIS method is better than regression analysis. Keywords: JCI, regression analysis, neuro fuzzy, RANFIS, genfis