Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices

We consider a new class of semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule-Walker equation to estimate trend function and spatio-temporal autoregressive coefficient matrices respectively. We also balance the over-determined and under-determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. The proposed methods are further illustrated using both simulation and case studies, the results also show that our estimator is stable among different sample size, and it performs better than the traditional method with known spatial weight matrices.

REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS

The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

THE CLUSNET ALGORITHM AND TIME SERIES PREDICTION

This paper describes a novel neural network architecture named ClusNet. This network is designed to study the trade-offs between the simplicity of instance-based methods and the accuracy of the more computational intensive learning methods. The features that make this network different from existing learning algorithms are outlined. A simple proof of convergence of the ClusNet algorithm is given. Experimental results showing the convergence of the algorithm on a specific problem is also presented. In this paper, ClusNet is applied to predict the temporal continuation of the Mackey–Glass chaotic time series. A comparison between the results obtained with ClusNet and other neural network algorithms is made. For example, ClusNet requires one-tenth the computing resources of the instance-based local linear method for this application while achieving comparable accuracy in this task. The sensitivity of ClusNet prediction accuracies on specific clustering algorithms is examined for an application. The simplicity and fast convergence of ClusNet makes it ideal as a rapid prototyping tool for applications where on-line learning is required.