Autoregressive Integrated Moving Average is a model that commonly used to model time series data. One model that can be modeled is Moving Average (MA). In this study, the estimation of parameters was performed to produce the model estimator parameter, where if the order component of the MA model is known, then the methods that can be used are the Ordinary Least Square (OLS) method, Moment method, and Maximum Likelihood method. But in fact, there are often assumption deviations when using the OLS method, one of which occurs heteroscedasticity (variant is not constant) which is produce a poor estimator. This study used both Moment and Maximum Likelihood method in estimating the parameter of the 1st Moving Average model, denoted by MA (1). The result showed that MA (1) parameter model using Moment method gave better result than Maximum Likelihood method. This can be seen from the value of Schwartz Bayesian Criterion (SBC) of both Moment and Maximum Likelihood method parameter estimator with magnified amount of data and various parameters values generated.

River water discharge is important information for water resources management planning, so it is necessary to develop river water discharge model as basis of its predictions. In order to get the result of predictions of river water discharge with high accuracy, it is developed a model of river water discharge based on the predictions of local climate (local rainfall and temperature) that are influenced by global climate conditions. Prediction of local climate is based on the Kernel nonparametric statistical downscaling model by utilizing GCM data. GCM data is a high dimensional global data, so data pre-processing is needed to reduce data dimension. It is done by CART algorithm. Statistical downscaling model is used to predict local rainfall and temperature. The prediction results are quite good with relatively small RMSE value. They are used to develop model of river water discharge. Modeling river water discharge is carried out using the Kernel nonparametric approach. The model of river water discharge produced is quite good because it can be used to predict river water discharge with relatively small RMSE.

This study was conducted with the aim of determining the semiparametric spline regression model in the analysis of factors that influence rice production in East Lombok District in 2014 and finding out what factors influence the rice production results. The method used was semiparametric spline regression, with the selection of the optimum knot points using Generalized Cross Validation. The results obtained indicate that the variable that significantly affects rice production was the height of the area above sea level, with the determination coefficient value of 99.71% and the RMSEP value of 41.65.

The inflation and interest rates in Indonesia have a significant impact on the country's economic development. Indonesian inflation and interest rates data are multivariate time series data that show activity over a certain period of time. Vector Autoregressive Integrated Moving Average (VARIMA) is a method for analyzing multivariate time series data. This method is a simultaneous equation modeling that has several endogenous variables simultaneously. This study aimed to model the inflation and interest rates data, from January 2009 to December 2016 and predict inflation and interest rates by using VARIMA method. The model obtained was the VARIMA(0,2,2) model, with estimated parameters using the maximum likelihood method. The choice of the VARIMA(0,2,2) model was based on the smallest AIC value of -4,2891, with a MAPE value for the inflation and interest rates forecasting were 6,04% and 1,84%, respectively, which indicates a very good forecast results.

This study was conducted by considering the data pattern that differs from each independent variable to the dependent variable. If only one estimator is used to estimate the nonparametric regression curve, the resulting estimator does not match the data pattern, less precise, and tends to produce large errors. Therefore, this study aimed to model the mixed truncated spline and kernel nonparametric regression on data and predict the population growth rate in West Nusa Tenggara Province by considering the Mean Absolute Percentage Error (MAPE). Based on the study conducted, relationships generated by x 1,x 2, x 7, x 8 formed specific patterns and were indicated to follow the spline approach’s characteristics. In contrast, the pattern generated by x 3, x 4, x 5, x 6, x 9 showed the data distribution with no specific pattern and were addressed to follow the kernel approach’s characteristics. The best model was obtained with the optimal bandwidth for each variable and 3 points of optimal knots. The mixed truncated spline and kernel nonparametric regression model was suitable for modeling and predicting population growth rate data in West Nusa Tenggara Province with a relatively high proportion and a high degree of accuracy.