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All Journal Media Statistika MATEMATIKA Journal of the Indonesian Mathematical Society
Herni Utami
Department of Mathematics Gadjah Mada University, Indonesia
Decision Sciences, Operations Research & Management Mathematics

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SECOND ORDER LEAST SQUARE ESTIMATION ON ARCH(1) MODEL WITH BOX-COX TRANSFORMED DEPENDENT VARIABLE Utami, Herni; -, Subanar
Journal of the Indonesian Mathematical Society Volume 19 Number 2 (October 2013)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.19.2.166.99-110

Abstract

Box-Cox transformation is often used to reduce heterogeneity and to achieve a symmetric distribution of response variable. In this paper, we estimate the parameters of Box-Cox transformed ARCH(1) model using second-order leastsquare method and then we study the consistency and asymptotic normality for second-order least square (SLS) estimators. The SLS estimation was introduced byWang (2003, 2004) to estimate the parameters of nonlinear regression models with independent and identically distributed errors.DOI : http://dx.doi.org/10.22342/jims.19.2.166.99-110
PENGARUH SUATU DATA OBSERVASI DALAM MENGESTIMASI PARAMETER MODEL REGRESI Utami, Herni; I, Ruri; abdurrakhman, abdurrakhman
MATEMATIKA Vol 5, No 3 (2002): Jurnal Matematika
Publisher : MATEMATIKA

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (54.254 KB)

Abstract

Observasi yang mempengaruhi model regresi sedemikian hingga elipsoid konfidensi untuk estimasi parameter regresinya menjadi kecil apabila observasi tersebut “dihilangkan” adalah observasi penting.  Sehingga observasi penting tersebut bisa merupakan observasi berpengaruh sesungguhnya atau bisa juga sebagai outlier. Salah satu cara menentukan observasi ke-i penting atau tidak, melihat  elipsoid konfidensi parameter model regresi linear dengan “menghilangkan”  observasi tersebut.
SELECTION OF INPUT VARIABLES OF NONLINEAR AUTOREGRESSIVE NEURAL NETWORK MODEL FOR TIME SERIES DATA FORECASTING Hermansah, Hermansah; Rosadi, Dedi; Abdurakhman, Abdurakhman; Utami, Herni
MEDIA STATISTIKA Vol 13, No 2 (2020): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/medstat.13.2.116-124

Abstract

NARNN is a type of ANN model consisting of a limited number of parameters and widely used for various applications. This study aims to determine the appropriate NARNN model, for the selection of input variables of nonlinear autoregressive neural network model for time series data forecasting, using the stepwise method. Furthermore, the study determines the optimal number of neurons in the hidden layer, using a trial and error method for some architecture. The NARNN model is combined in three parts, namely the learning method, the activation function, and the ensemble operator, to get the best single model. Its application in this study was conducted on real data, such as the interest rate of Bank Indonesia. The comparison results of MASE, RMSE, and MAPE values with ARIMA and Exponential Smoothing models shows that the NARNN is the best model used to effectively improve forecasting accuracy.
Co-Authors Abdurakhman Abdurakhman ABDURRAKHMAN ABDURRAKHMAN, ABDURRAKHMAN Dedi Rosadi Hermansah Hermansah, Hermansah I, Ruri Subanar -