Statistical downscaling (SD) is a statistical technique used to predict local scale rainfall based on global atmospheric circulation. The global scale climate variable used is precipitation from GCM (Global Circulation Model). However, the precipitation data of GCM outputs have a large dimension, giving rise to multicollinearity in the data. This problem is handled by the Principal Component Regression (PCR) method. In addition, the SD models have heterogeneous error variances. The dummy variable is added to the PCR models to solve the problem. Hierarchical (k-means) and non-hierarchical cluster techniques (average linkage, median linkage, and ward linkage) are used in modeling to determine rainfall data groups. Furthermore, the group formed is the basis of the formation of dummy variables. This study aims to estimate local rainfall data in Pangkep district as a salt-producing area in South Sulawesi. There are 4 dummy variables based on the 5 groups formed. Dummy variables are able to improve predictions from the PCR models. R2 values of the PCR-dummy models (ranging from 89.89% to 95.58%) are relatively higher than the PCR models (ranging from 55.87% to 57.61%). This result is also consistent with the model validation stage. The PCR-dummy models based on non-hierarchical cluster techniques (k-means) are better than the PCR-dummy models based on cluster hierarchy techniques. In general, the best model is the PCR-dummy model of the non-hierarchical cluster technique (k-means ) and involves 4 main components.

Liu-Type Regression (LTR) is one of the statistical methods to overcome multicollinearity in multiple regression models. LTR is the development of Ridge regression and Liu estimator. When there is a strong collinearity, selected k parameter in the ridge regression does not fully overcome the multicollinearity. This study aimed to estimate the rainfall data in Pangkep Regency (as response variable) with LTR approach on Statistical Downscaling (SD) models. Precipitation (as predictor variables) is the result of a simulation of a grid on the Global Circulation Model (GCM). This study uses a size 8 8 grid of GCM (64 predictor variables) over an area of Pangkep Regency so that there is a high multicollinearity. Three dummy variables were determined from k-means cluster technique used as predictor variables to overcome the heterogeneity of residual variance. LTR model with dummy variables are able to explain the diversity of rainfall data properly. The value of R2 produced ranges 85.23% -88.99% with Root Mean Square Error (RMSE) ranges 117.732-136.377. Validation of the model generates a high correlation value between the actual rainfall and alleged rainfall period of 2017 (about 0.977-0.979). The value of Root Mean Square Error Prediction (RMSEP) produced lower (about 57.625-61.120). SD analysis was also performed with and without the dummy variable in the Ridge regression and LTR. In general, LRT models with dummy (k = 0.652, d = -0.799) is the best model based on the value of R2, RMSE, correlation, and RMSEP.

The Poisson hidden Markov model is a model that consists of two parts. The first part is the cause of events that are hidden or cannot be observed directly and form a Markov chain, while the second part is the process of observation or observable parts that depend on the cause of the event and following the Poisson distribution. The Poisson hidden Markov model parameters are estimated using the Maximum Likelihood Estimator (MLE). But it is difficult to find analytical solutions from the ln-likelihood function. Therefore, the Expectation Maximization (EM) algorithm is used to obtain its numerical solutions which are then applied to life insurance data. The best model is obtained with 2 states or m = 2 based on the smallest Bayesian Information Criterion (BIC) value of 338,778 and the average predicted number of claims arrivals is 0.385 per day.

Harga saham selalu berfluktuasi dari waktu ke waktu sehingga sulit untuk diprediksi. Prediksi terhadap fluktuasi harga saham memberikan dampak yang signifikan bagi perusahaan, investor maupun pemegang saham dalam mengambil keputusan terbaik untuk pilihan investasi yang memberikan profit maksimal. Beberapa negara mempunyai indeks saham yang secara umum menjadi ukuran untuk mengetahui pergerakan harga saham sahamnya. Indeks saham LQ45 dan IHSG dari Indonesia, S&P 500 milik Amerika Serikat, Nikkei 225 dari Jepang, serta Shenzhen dari China merupakan beberapa contoh indeks saham yang memiliki valuasi terbesar di dunia. Pemodelan peluang transisi rantai Markov adalah salah satu cara untuk memprediksi indeks harga saham. Pemodelan menggunakan rantai Markov ini efektif untuk dilakukan karena kemampuannya dalam memprediksi dengan model yang sederhana dibandingkan dengan model lainnya. Selanjutnya, digunakan metode Monte Carlo untuk memodelkan peluang transisi rantai Markov berdasarkan bangkitan nilai dari distribusi Multinoulli untuk memprediksi keadaan dan harga penutupan indeks saham untuk waktu yang akan datang. Disimpulkan bahwa dari kedua model antara rantai Markov dan regresi linear yang diterapkan pada data indeks saham IHSG, LQ45, Nikkei 225, Shenzhen, dan S&P 500, diperoleh bahwa model rantai Markov adalah yang paling memiliki keakuratan paling baik berdasarkan ukuran Mean Absolute Percent Error (MAPE).