REML in time series models: Applications to unified inference in moderate and near integrated autoregressions, dynamic panels, cointegrated systems and non-linear IV regressions

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The proposed research demonstrates how the restricted likelihood approach can resolve several well known estimation and inference problems. For the inference problem of a near integrated process with deterministic components, this research provides a framework for unified inference based on the chi-squared distribution for autoregressive processes with deterministic components regardless of whether they are stationary, moderate integrated, near integrated or integrated processes. A weighted least squares approximate restricted likelihood is provided for multivariate time series models so that a computationally simple method with attractive theoretical properties is available. The proposal also includes using the restricted likelihood for the incidental parameter problem in dynamic panel data model. Research is also planned to explore the restricted likelihood for non-linear models for which there do not seem to be any results available. This research will help to build a bridge between statistics and economics. Restricted likelihood has existed for almost four decades and been routinely used in linear mixed models. While the restricted likelihood has historically been used for bias reduction, recent research has also shown that the restricted likelihood based likelihood ratio test statistic has nice properties in nonparametric models. However, this large body of work on the restricted likelihood has largely ignored its potential use in time series models with only very few exceptions including the PI's research under the previous grant. This proposal is a continuing dialogue with researchers and practitioners in statistics as well as econometricians on the applications of restricted likelihood. A number of projects are presented with the aim of facilitating the application of restricted likelihood in the most widely used econometric models.