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This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

We formulate generalized maximum entropy estimators for the general linear model and the censored regression model when there is first order spatial autoregression in the dependent variable. Monte Carlo experiments are provided to compare the performance of spatial entropy estimators relative to classical estimators. Finally, the estimators are applied to an illustrative model allocating agricultural disaster payments.

The authors propose a semiparametric approach for testing independence between two infinite-order cointegrated vector autoregressive series (IVAR(∞)). The procedures considered can be viewed as extensions of classical methods proposed by Haugh (1976, JASA) and Hong (1996b, Biometrika) for testing independence between stationary univariate time series. The tests are based on the residuals of long autoregressions, hence allowing for computational simplicity, weak assumptions on the form of the underlying process, and a direct interpretation of the results in terms of innovations (or shocks). The test statistics are standardized versions of the sum of weighted squares of residual cross-correlation matrices. The weights depend on a kernel function and a truncation parameter. Multivariate portmanteau statistics can be viewed as a special case of our procedure based on the truncated uniform kernel. The asymptotic distributions of the test statistics under the null hypothesis are derived, and consistency is established against fixed alternatives of serial cross-correlation of unknown form. A simulation study is presented which indicates that the proposed tests have good size and power properties in finite samples.

The purpose of this paper is two-fold. First, on a theoretical level we introduce a series-type instrumental variable (IV) estimator of the parameters of a spatial first order autoregressive model with first order autoregressive disturbances. We demonstrate that our estimator is asymptotically efficient within the class of IV estimators, and has a lower computational count than an efficient IV estimator that was introduced by Lee (2003). Second, via Monte Carlo techniques we give small sample results relating to our suggested estimator, the maximum likelihood (ML) estimator, and other IV estimators suggested in the literature. Among other things we find that the ML estimator, both of the asymptotically efficient IV estimators, as well as an IV estimator introduced in Kelejian and Prucha (1998), have quite similar small sample properties. Our results also suggest the use of iterated versions of the IV estimators.

This paper aims to investigate spillover effects of public capital stock in a production function model that accounts for spatial dependencies. In many settings, ignoring spatial dependency yields inefficient, biased and inconsistent estimates in cross country panels. Although there are a number of studies aiming to estimate the output elasticity of public capital stock, many of those fail to reach a consensus on refining the elasticity estimates. We argue that accounting for spillover effects of the public capital stock on the production efficiency and incorporating spatial dependences are crucial. For this purpose, we employ a spatial autoregressive stochastic frontier model based on a number of specifications of the spatial dependency structure. Using the data of 21 OECD countries from 1960 to 2001, we estimate a spatial autoregressive stochastic frontier model and derive the mean indirect marginal effects of public capital stock, which are interpreted as spillover effects. We found that spillover effects can be an important factor explaining variations in technical inefficiency across countries as well as in explaining the discrepancies among various levels of output elasticity of public capital stock in traditional production function approaches.

This chapter proposes a test for a parametric specification of the autoregressive function of a given stationary autoregressive time series. This test is based on the integrated square difference between the empirical distribution function estimate and a convolution-type distribution function estimate of the stationary distribution function obtained from the autoregressive residuals. Some asymptotic properties of the proposed convolution-type distribution function estimate are studied when the model’s innovation density is unknown. These properties are in turn used to derive the asymptotic null distribution of the proposed test statistic. We also discuss some finite sample properties of the test statistic based on the block bootstrap methodology. A simulation study shows that the proposed test competes favorably with some existing tests in terms of the empirical level and power.

For this discussion, assume there are n sample observations of the dependent variable y at unique locations. In spatial samples, often each observation is uniquely associated with a particular location or region, so that observations and regions are equivalent. Spatial dependence arises when an observation at one location, say y i is dependent on “neighboring” observations y j, y j∈ϒi. We use ϒi to denote the set of observations that are “neighboring” to observation i, where some metric is used to define the set of observations that are spatially connected to observation i. For general definitions of the sets ϒi,i=1,…,n, typically at least one observation exhibits simultaneous dependence, so that an observation y j, also depends on y i. That is, the set ϒj contains the observation y i, creating simultaneous dependence among observations. This situation constitutes a difference between time series analysis and spatial analysis. In time series, temporal dependence relations could be such that a “one-period-behind relation” exists, ruling out simultaneous dependence among observations. The time series one-observation-behind relation could arise if spatial observations were located along a line and the dependence of each observation were strictly on the observation located to the left. However, this is not in general true of spatial samples, requiring construction of estimation and inference methods that accommodate the more plausible case of simultaneous dependence among observations.

We analyze spatio-temporal data on U.S. unemployment rates. For this purpose, we present a family of models designed for the analysis and time-forward prediction of spatio-temporal econometric data. Our model is aimed at applications with spatially sparse but temporally rich data, i.e. for observations collected at few spatial regions, but at many regular time intervals. The family of models utilized does not make spatial stationarity assumptions and consists in a vector autoregressive (VAR) specification, where there are as many time series as spatial regions. A model building strategy is used that takes into account the spatial dependence structure of the data. Model building may be performed either by displaying sample partial correlation functions, or automatically with an information criterion. Monthly data on unemployment rates in the nine census divisions of the U.S. are analyzed. We show with a residual analysis that our autoregressive model captures the dependence structure of the data better than with univariate time series modeling.