Compact Autoregressive Network

Autoregressive networks can achieve promising performance in many sequence modeling tasks with short-range dependence. However, when handling high-dimensional inputs and outputs, the huge amount of parameters in the network lead to expensive computational cost and low learning efficiency. The problem can be alleviated slightly by introducing one more narrow hidden layer to the network, but the sample size required to achieve a certain training error is still large. To address this challenge, we rearrange the weight matrices of a linear autoregressive network into a tensor form, and then make use of Tucker decomposition to represent low-rank structures. This leads to a novel compact autoregressive network, called Tucker AutoRegressive (TAR) net. Interestingly, the TAR net can be applied to sequences with long-range dependence since the dimension along the sequential order is reduced. Theoretical studies show that the TAR net improves the learning efficiency, and requires much fewer samples for model training. Experiments on synthetic and real-world datasets demonstrate the promising performance of the proposed compact network

Consistent and Non-Degenerate Model Specification Tests Against Smooth Transition Alternatives

In this paper we develop a test of functional form that is consistent against any deviation from the null specification, and directs power towards a class of nonlinear "smooth transition" functional forms. Of separate interest, we provide new details regarding when and whether consistent parametric tests of functional form are asymptotically degenerate. A test of linear autoregression against smooth transition alternatives is never degenerate. Moreover, a test of Exponential STAR has surprising power and non-degeneracy attributes entirely associated with the choice of threshold. In a simulation experiment in which all parameters are randomly selected the proposed test has power nearly identical to the most powerful tests for true STAR, neural network and SETAR processes, and dominates popular tests. We apply the test to monthly U.S. output, money supply, prices and interest rates.smooth transition, consistent test, nondegenerate test, nonlinear, neural networks