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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 : MEDIA STATISTIKA

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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.
ESTIMASI MODEL UNTUK DATA DEPENDEN DENGAN METODE CROSS VALIDATION Tarno, Tarno
MEDIA STATISTIKA Vol 1, No 2 (2008): Media Statistika
Publisher : Jurusan Statistika FSM Undip

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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
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 : Jurusan Statistika FSM Undip

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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
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 : Jurusan Statistika FSM Undip

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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
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

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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
ANALISIS DATA RUNTUN WAKTU DENGAN METODE ADAPTIVE NEURO FUZZY INFERENCE SYSTEM (ANFIS) Saputra, Arsyil Hendra; Tarno, Tarno; Warsito, Budi
Jurnal Gaussian Vol 1, No 1 (2012): Wisuda Periode Oktober 2012
Publisher : Jurusan Statistika UNDIP

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Abstract

One popular method of time series analysis is ARIMA. The ARIMA method requires some assumptions; residual of model must be white noise, normal distribution and constant variance. The ARIMA model tends to be better for time series data which is linear. Whereas for the nonlinear time series data have been widely studied by nonlinear methods, one of that is Adaptive Neuro Fuzzy Inference System or ANFIS. The ANFIS method is a method that combines techniques Neural Network and Fuzzy Logic. In this thesis discussed the ANFIS method specifically for the analysis of time series data that have characteristics such as stationary, stationary with outlier, non stationary and non stationary with outlier, and the data of Indonesian palm oil prices is used as a case study. The ANFIS results which were obtained are compared with the results of ARIMA method by the value of RMSE. Based on the analysis and discussion, it is obtained that the results of ANFIS method are better than the results of ARIMA method.
PEMODELAN LAJU INFLASI DI PROVINSI JAWA TENGAH MENGGUNAKAN REGRESI DATA PANEL Apriliawan, Dody; Tarno, Tarno; Yasin, Hasbi
Jurnal Gaussian Vol 2, No 4 (2013): Wisuda Periode Oktober 2013
Publisher : Jurusan Statistika UNDIP

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Panel regression is a regression which is a combination of cross section and time series. To estimate the panel regression there are 3 approaches, the common effect model (CEM), the fixed effect model (FEM) and the random effect model (REM). In the CEM, the parameters were estimated using the Ordinary Least Square (OLS). In the FEM, the parameters estimated by OLS through the addition of dummy variables. At REM, error is assumed random and estimated by the method of Generalized Least Square (GLS). This study aims to analyze the factors that influence inflation in the Central Java province using panel regression. Based on test result of panel regression, the appropriate model is the CEM. The parameters of model are estimated by using OLS the cross section weights. The model show that the Consumer Price Index (CPI), Minimum Salary of City/Regency (MSCR) and the economic growth significantly effect on percentage of inflation in Central Java Province.
ANALISIS INTERVENSI DAN DETEKSI OUTLIER PADA DATA WISATAWAN DOMESTIK (Studi Kasus di Daerah Istimewa Yogyakarta) Budiarti, Lenny; Tarno, Tarno; Warsito, Budi
Jurnal Gaussian Vol 2, No 1 (2013): Wisuda Periode Januari 2013
Publisher : Jurusan Statistika UNDIP

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The tourist data is very interesting to be studied because the Indonesian tourism sector is an activator of the national economic which is potential to push higher economic growth in the future. Therefore, the forecast about tourist data is very needed for tourism business. The tourist data tend to fluctuate caused by many factors that affect the number of tourists extremely in an area, such as disasters, government regulation, social stability, violence and terrorism. That the extreme data can be assessed using intervention analysis and outlier detection. Intervention model is a time series model that can be used to forecast data consist of intervention of internal and external factors. In the intervention model, there are two kinds of intervention function, i.e., step and pulse functions. Step function is a form of intervention occurred in period of time while the pulse function is a form of intervention occurred only in a certain time. For the outlier detection, there are four types, such as additive outlier (AO), innovational outlier (IO), level shift (LS) and temporary change (TC). As an empirical studies was conducted by the domestic tourists data in Yogyakarta from January 2006 until December 2010 who staying on five-star hotels and motel throughout Yogyakarta. Based on the result of this research, known that the intervention occurred on January 2010 using the pulse function with MSE value 1172. Meanwhile based on the outliers detection, known any five outliers but only four outliers that significant included to the intervention model with MSE value 523,7167. So, the intervention model and outlier detection are chosen as a the best model based on the smallest MSE criterion. Keywords: Domestic tourists, intervention model, pulse function, outlier detection
PENENTUAN TREN ARAH PERGERAKAN HARGA SAHAM DENGAN MENGGUNAKAN MOVING AVERAGE CONVERGENCE DIVERGENCE (Studi Kasus Harga Saham pada 6 Anggota LQ 45) Raditya, Tri Murda Agus; Tarno, Tarno; Wuryandari, Triastuti
Jurnal Gaussian Vol 2, No 3 (2013): Wisuda Periode Agustus 2013
Publisher : Jurusan Statistika UNDIP

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One of many examples of technical indicator that frequently used for stock price analysis is Moving Average Convergence Divergence (MACD). MACD generates two signal called goldencross and deathcross are used to find the reversal momentum of stock price trend movement. Goldencross as a oversold point marker serves to give a buying signal. While, deathcross as a overbought point marker serves to give a selling signal. Research on six stocks member of LQ45 (ANTM, BWPT, MNCN, TINS, BJBR, and LPKR) during the period January 1 until October 31, 2012 managed to prove the accuracy of the signal formed by MACD signal. By applying the MACD Indicator consistently, investors can get a percentage of profit above the actual inflation rate in 2012 by Indonesian Bank. On these  results, the goldencross and deathcross signal give a good performance as tool of technical analysis for determining the trend of the direction of stock price movements
ANALISIS DATA RUNTUN WAKTU MENGGUNAKAN METODE WAVELET THRESHOLDING Wibowo, Yudi Ari; Suparti, Suparti; Tarno, Tarno
Jurnal Gaussian Vol 1, No 1 (2012): Wisuda Periode Oktober 2012
Publisher : Jurusan Statistika UNDIP

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Latterly, wavelet is used in various application of statistics. Wavelet is a method without parameter which used in signal analysis, data compression, and time series analysis. Wavelet thresholding is a method which reconstructing the largest number of wavelet coefficients. Only the coefficients are greater than a specified value which taken and the rest coefficients are ignored, because considered null. Certain value is called the threshold value. The level of smoothness estimation are determined by some factor such as wavelet functions, the type of thresholding functions, level of resolutions and threshold parameters. But most dominant factor is threshold parameter. Because that was required to select the optimal threshold value. At the simulation study was analyzing of the stasioner, nonstasioner and nonlinier data. Wavelet thresholding method gives the value of Mean Square Error (MSE) which is smaller than the ARIMA. Wavelet thresholding is considered quite so well in the analysis of time series data.