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This paper proposes a new model-based approach to small area estimation of general finite-population parameters based on grouped data or frequency data, often available from sample surveys. Grouped data contains information on frequencies of some pre-specified groups in each area, for example, the numbers of households in the income classes. Thus, grouped data provide more detailed insight into small areas than area-level aggregated data. A direct application of the widely used small area methods, such as the Fay–Herriot model for area-level data and nested error regression model for unit-level data, is not appropriate since they are not designed for grouped data. Our novel method adopts the multinomial likelihood function for the grouped data. In order to connect the group probabilities of the multinomial likelihood and the auxiliary variables within the framework of small area estimation, we introduce the unobserved unit-level quantities of interest. They follow a linear mixed model with random intercepts and dispersions after some transformation. Then the probabilities that a unit belongs to the groups can be derived and are used to construct the likelihood function for the grouped data given the random effects. The unknown model parameters (hyperparameters) are estimated by a newly developed Monte Carlo EM algorithm which uses an efficient importance sampling. The empirical best predicts (empirical Bayes estimates) of small area parameters are calculated by a simple Gibbs sampling algorithm. The numerical performance of the proposed method is illustrated based on the model-based and design-based simulations. In the application to the city-level grouped income data of Japan, we complete the patchy maps of the Gini coefficient as well as mean income across the country. [ABSTRACT FROM AUTHOR]

Abstract: Fluctuations in the stock market follow the principle of volatility clustering in which changes are cataloged by similarity; as such, large changes tend to follow large changes, and small changes tend to follow small changes. This clustering is one of the major reasons why many generalized autoregression conditional heteroscedasticity (GARCH) models do not forecast the stock market well. In this paper, an adaptive Fuzzy-GARCH model with particle swarm optimization (PSO) is proposed to solve this problem. The adaptive Fuzzy-GARCH model refers to both GARCH models and the parameters of membership functions, which are determined by the characteristics of market itself. Here, we present an iterative algorithm based on PSO to estimate the parameters of the membership functions. The PSO method aims to achieve a global optimal solution with a rapid convergence rate. The three stock markets of Taiwan, Japan, and Germany were analyzed to illustrate the performance of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we derive a new class of flexible threshold asymmetric Generalized Autoregression Conditional Heteroskedasticity (GARCH) models. We use this tool for analysis and modeling of the properties that are apparent in many financial time series. In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an asymmetric GARCH model. Our simulations use stock market data from the Taiwan weighted index (Taiwan), the Nikkei 225 index (Japan), and the Hang Seng index (Hong Kong) to illustrate the performance of our proposed method. From the simulation results, we have determined that the forecasting of volatility performance is significantly improved if the leverage effect of clustering is considered along with the use of expert knowledge enabled by the GARCH model. [Copyright &y& Elsevier]