METODE ESTIMASI SECOND-ORDER LEAST SQUARE PADA MODEL AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTIC DAN TRANSFORMASINYA

• Main Authors: , HERNI UTAMI, , Drs. Pekik Murwantoro, M.S.,Ph.D
• Format: Theses and Dissertations NonPeerReviewed
• Published: [Yogyakarta] : Universitas Gadjah Mada 2014
• Subjects: ETD
• Online Access: https://repository.ugm.ac.id/132894/; http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=73439

Autoregressive Conditional Heteroskedasticity (ARCH) processes have been widely used to analysis of finance time series. Many finance time series exhibit periods of unusually large volatility followed by periods of relative tranquility. This suggests that the variance are serially correlated. Estimate for model is a important step in time series analysis. In this research, we used second-order least square (SLS) estimation method to estimate ARCH model. SLS estimation method was introduced by Wang & Leblanc (2008) to estimate the parameters of nonlinear regression model with errors are independent and identically distributed. SLS estimators are determined by minimizing the square distance of the response variable to its first conditional moment and the square response variable to its second conditional moment of response variable. Using SLS estimation method for estimating the ARCH model will obtain estimators for the mean and the variance regression simultaneously. We studied the consistency and asymptotic normality for second-order least square (SLS) estimators. Least square is a estimation method that be used to estimate ARCH model with minimizing sum of square error. It has finite sample properties are worse than SLS estimation. The convergence speed of LS estimator is slower than SLS estimator. The research found that asymptotically SLS estimator more efficient than LS estimator for ARCH model. The results of Monte Carlo simulation show performance of SLS estimator better than LS estimator. Box-Cox transformation is widely used to reach a condition in the time series analysis. For examples: stationarity, lenearity, etc. Especially in the proces ARCH, transformation can give the effect on the SLS estimation of ARCH model. In this research, we study the effects of Box-Cox transformation on the SLS estimation of the ARCH model. A Monte Carlo study will be conducted to show bias and varience xv xvi of the estimation obtained after Box-Cox transformation is applied on the observed dependent variable.